Malness - I'm from Lincoln and have lived here all my life. I don't personally know each place you listed, but I can tell you what I've heard. I will try to touch on the neighborhoods also.
Most of the "iffy" areas that are mentioned are south of 'O' Street. As a rough guideline, "iffy" parts start around J steet and continue south between 9th street and 27th. Of course, there are areas in this grid that are safe and there are areas outside of this grid that are just as, if not moreso, unsafe.
Lincoln is a real hit or miss city when it comes to apartments. While the places you mentioned are nice, they can not only get pretty expensive (I dont know if that's a concern for you or not) but they can also have waiting lists.
I wouldn't suggest any apartments close to the capitol or the police station, atleast not right away. After you get settled down and start to understand and see more of the neighborhoods, you can pick and choose which apartments (and neighborhoods) are best.
Haymarket Lofts are extremely nice, but they have a waiting list. As do The Grainger Building and The Hardy Building. Last time I heard, it was over a year. You can try, but I'm pretty darn sure you won't be able to rent there. The Haymarket though, (Which is where these three places are located) is a very "yuppie" area. It's pretty safe compared to south of downtown and there are a bunch of things to do.
Sky Park is also considered extremely nice. It may be alittle farther than you like though. It's roughly 12 blocks from campus, which doesn't seem like much until you walk there in winter.

The neighborhood is considered pretty nice for this area. I don't know if I, being a woman, would walk around alone at night, but I don't think that I would freak out if I had to. Does that make sense?
Centerstone and Georgian Place are both pretty nice as well. They are both located in the heart of downtown Lincoln and there may be waiting lists for them as well. They are both relitively old buildings that have alot of history to them. Very beautiful architecture. Being in such a busy area, these apartments are pretty safe. You may have an run in or two with a drunkie, but you shouldn't have any bigger problems than that.
I don't have any knowledge of Rochambeau, I'm sorry. I do know though that 12th and K St. isn't the best area. It certainly is not the worst, but I, personally, wouldn't live there.
It may seem like I'm trying to make just south of 'O' St. out to be this not-so-safe place. That isn't totally true. I know alot of people that live around these areas and are more safe than I am. But since you are not going to be able to check these places out before you move, I am just trying to tell you where you have to be aware. Pretty much, if you have common sense and keep your eyes open, you shouldn't really have any problems.
A few blocks may be incredibly safe and seem like paradise, while just a block away there's drug deals and crap like that going down. It's incredibly hit or miss in this area of Lincoln.
Our busses are pretty good for college students, as there are stops all over downtown. The problem though is they stop running at around 6pm (I think) and don't run on Sundays. (I haven't taken a bus is so long. I don't know if they run on Saturdays. I can't remember.)
I would stay away from Vine St around 25th. It is decently close to campus and so it houses students, but it has a rep for being a dangerous part of Lincoln.
I wish you luck with your search!! If you need any more info, you can PM me and I will try to help you if I can.