One thing you'll find easily in Providence are places to eat, especially if you hop over to the Eastside or Federal Hill. Downtown has a couple places, too. If you're looking to spend lots of time in restaurants, Providence will probably not disappoint. When it comes to bookstores, I'd say you're better off looking somewhere else. For shopping, there's the Providence Place Mall if you're looking for your standard mainstream fare. You'll be able to find a couple more interesting shops if you know where to look but it's honestly not too much to write home about. It really depends what you're looking for.
About the vibe of Providence, that's tough to say. I find it varies a lot. Sometimes it feels as if Providence is perpetually stuck in some kind of provincial mire, sometimes there are downright cosmopolitan developments. In my opinion, Providence is lacking an identity, it doesn't really know what it wants to be. That's not necessarily a good thing.
I don't find people in Providence particularly friendly or unfriendly, honestly. It's a mixed crowd and you'll get what you put into the equation. Not too many shiny happy people here, but it's not a bunch of jerks either.
Crime isn't a huge problem, no. I do think though that it's a bit iffy, especially if you choose to live Downtown. You'll need some common sense in Providence and some kind of idea where to go or which areas to avoid, especially at night. But during the day, no, it's not very scary.
When it comes to gay people - yes, Providence seems to be pretty gay friendly and relatively accepting. There are bars catering to the gay crowd, there's our mayor etc. Gay Pride happened right Downtown a couple weeks ago and I don't think there were any major incidents.
Nice areas to live would probably be the Eastside and Federal Hill. Downtown is tricky and certainly not for everybody, it depends a lot on what you expect from a Downtown area. If it's restaurants, parties and bars, yes, come live here. If it's some kind of mini Manhattan...run and don't look back.
A nice studio should probably run you about 700 dollars, I'd say. Maybe a little less, it really depends on the area you're looking to live in. I'd think you would enjoy the Eastside, so check out craigslist.
On jobs...I don't know if IT jobs are particularly strongly in demand these days. I'd think you'd probably have a decent chance. Be warned though, the job market in RI is not friendly at the moment. We aren't doing very well when it comes to employment. Also, getting a job in RI is not only about your qualifications but very much about who you know in the state and who they know. It's very difficult for 'outsiders' to get a foot in the door.
Hope that helps.
Honestly though, I think you're crazy to leave NYC for Providence.
Good luck.