My family just moved to Mt. Vernon over the summer, for my husband's job at Cornell College. We were most recently elsewhere in the midwest for a few years, but before that lived in West L.A. for a decade. Since others have given you some highlights about Iowa City I thought I could answer your questions about Mt. Vernon more specifically, especially from a new-comer's perspective (I think either town would be a good choice, just depending on your personal specifications).
1. We have had a really easy time getting to meet new people, partly because of our connection to the College but also because it is a small, social town. There are a ton of local events (an arts festival in the summer, special trick-or-treating and a community dinner in adjoining Lisbon in the fall, a winter "Magical Night" coming up after Thanksgiving to name a few) where you will meet and then run into folks. People are very friendly--I think there tends to maybe be more turn-over than you might otherwise find in a town this size because of the college, so everyone is used to new people. Our very first week here, our new neighbors invited us to a huge picnic hosted by several couples where we met dozens of people, including a very cool couple who had just relocated from Colorado (not for Cornell) who turned out to have a daughter in our twins' preschool class.
I'm not Christian, and have not found the lack of church-going to be an issue--as someone else said about Iowa City, no one has even asked. Now, if you were an observant member of another religion, that might be a problem, as I don't believe there are any temples, synagogues, mosques, etc. here--you would need to go "into town" for that.
I think if you were to move here, some things you could do to be sure to meet people would be to maybe volunteer for something (there's a community theater, volunteer fire department, lots of local events as I mentioned, whatever your cup of tea), and try to hook up with someone who is plugged into the community. There are a number of sort of informal community boosters in town who know everyone and are happy to introduce people around (we're very lucky to live next door to one of these). Also, just talk to your neighbors, shop clerks, and so forth. Once people hear that you're new, they will most likely start trying to "set you up" with other people they think you'd like (people here really like to network--if you mention you're looking for a job, EVERYONE will know someone you should talk to in whatever field you're in).
Of course once your baby arrives, you will have an instant ice-breaker. We have met several people through our twins' preschool, and just yesterday I took my kids to the big park after school for the first time and struck up a conversation with the two other families there. If we had gotten it together to go before the temperature dropped into the 50s, I'm sure we could have been having play dates by now.
2. I do find Mt. Vernon to be quite progressive and tolerant, at least the parts that I have seen. The College really dominates the town, and of course the professors come from universities all over the country and pretty much fit the liberal academic paradigm. Most families seem to be two-income, with lots of professional women. The College Chaplain does blessing ceremonies for same-sex couples, but I don't know if there is any sizable gay population in Mt. Vernon outside the college. The city seems very environmentally aware--for example, recycling here is free (it's mixed recycling, with practically everything included) while trash pickup costs $2 a bag. A new environmental law practice just opened in town, too--they are currently suing to stop a nearby coal mining operation, I believe. I'm sure that the more stereotypically conservative, religious rural Iowa element is present here, too, but it definitely does not dominate the town.
A couple of other things I really like about Mt. Vernon: For such a small town, there really do seem to be tons of things to do. As you mention, the downtown is adorable--fun shopping during the day, and also much livelier than most small towns, with the Lincoln Cafe and Wine Bar etc. actually creating something of a local nightlife. It really reminds me of a beach resort town, just without the beach. In addition to the full-on events I mentioned above, there are also a tremendous number of cool, quirky community things, like the "walking tour of the universe" and sledding down one of the downtown streets in the winter. I've actually told people that I've basically moved to Stars Hollow (which will mean something to you only if you ever watched Gilmore Girls). Of course, for small children, I think Mt. Vernon is wonderful. (Ours are 5, 5, and 1.5.)
Second, I love how you can really walk to practically everything--and people do. It seems to me that people in Mt. Vernon are less likely to be obese than what I have observed in other parts of Iowa, and I suspect that this is partly due to all the walking. We can walk to the bank, the movie theater, ballet lessons, restaurants, etc. And there is at least one of almost every service--acupuncture, post office, drugstore, video store, photographer etc.
Third, it feels very safe. In the summer you will see kids who have walked downtown to get an ice cream, ten-year-olds waiting to walk their six-year-old sibling home from a class, and so forth, which are things I would not have felt comfortable letting my children do in our previous mid-sized college town, let alone L.A. But here they don't have to go through a "bad part of town" (or much of any part of town, lol) to get to something interesting, and you can be pretty sure that they will be in shouting distance of someone they know the whole way.
Also, a sort of positive--the drives to both Iowa City and Marion (the closest point with all the modern conveniences) are really scenic, at least during daylight in clear weather (can be a little scary in a raging thunderstorm at night). I love the little herds of cows grazing under trees next to a meandering stream--it really looks like those "Good Cheese Comes from Happy Cows" ads--and I'm sure that one of the farmers between MV and IC is an artist, given how gorgeously the fields of beans and corn have been planted.
OK, so the downsides I've seen to Mt. Vernon: The first, and hardest for me, is the lack of racial diversity. I'm a person of color, and this is by far the whitest town I have ever lived in. I have not encountered any overt racism (like I said, most of the people we know are QUITE liberal). However, it is a little uncomfortable and it bothers me that my children are in such a homogeneous school system. I'm also concerned that almost all of Cornell's faculty/staff of color have chosen to live elsewhere--I don't know if there is more racism out there that I haven't run into yet (we've only been here a few months) or if it's just that no one wants to be the first drop in the bucket. I think it's probably at least partly the latter, since we are seriously considering moving to IC down the road for just that reason. I have been trying to figure out a way to get a critical mass of us to stay put--not sure what the magic number to reach the tipping point would be, though!
The second downside is actually the flipside to the positives I mentioned above about meeting people--everyone knows everyone, and people are really social. I sometimes want to be a little hermit-like, which is a lot harder when the people handing you take-out actually know you, and virtual strangers are inviting you out to dinner left and right. And heaven forbid we do anything embarassing in public! I was talking to someone today who said that when her husband fell and broke his arm, she first heard it from someone else in town who was expressing her condolences, because "word had spread". We haven't encountered anything like that yet, but I'm sure it's just a matter of time.
Third, while most of the necessities of life can be found in town you do have to drive to IC or CR for a lot of things--mall shopping, first run movies, lots of theater and art, anything late night. This doesn't bother us that much, because frankly we had to drive at least as many minutes (20-45) for most things when we were in L.A., but it drives my Mom nuts--she's used to everything being within ten minutes in her mid-sized city. These last two I think are pretty much the way of things in any small town, not specific to Mt. Vernon.
Oh, and I don't know anything about a big drug problem in the high school--or in the college, either. I do know that there's a fair amount of alcohol use among the college population, as with most U.S. colleges, but I tend to doubt that cocaine and meth use is a lot more widespread proportionately than at U of I. (It may just be that I haven't been here long enough, but I'd be a little surprised to find drugs really running rampant in the school without my husband having heard anything about it at all, as Cornell really keeps a close eye on students--they even report to the Dean whenever a student has more than one unexplained absence. They have this "one class at a time" thing where students take just one class for a month--they're in the same small class several hours a day, five days a week, so profs really get to know their students, which is the way the College wants it.) In any case, I'm not going to make a decision about where to live based on what high school kids might get up to when they're bored until my kids are closer to high school age, and I have a better idea of what THEY might get up to (and just how bored they are).
I hope all that is useful in some way! If you do decide to move to Mt. Vernon, let us know and I will look you up when you get here--I would love to be the experienced resident showing the newcomer around, instead of the other way

.
P.S. I really hope there's nothing in this post that would offend longer-term Mt. Vernon residents, or that's grossly inaccurate, since I'm sure there are already at least fifty people in town who could easily identify me from this post. If any of you are reading this--I love Mt. Vernon, and Mt. Vernonites! Please don't hold anything I said against Mr. Nedibes at tenure review!