UIC is a 4 year program, but the other schools you mention are for Associates - do you want a 4 year, or do you want a 2 year?
For a 4 year - there is NIU in DeKalb, they have a very good Nursing school - not sure the waiting list. You could take pre-reqs at a community college and then transfer there. There are also many other 4 year schools not too far from the city - Eastern, Western, Northern, UofI in champaign, etc.
When looking at associates, some require you to live in district (like COD) and some do not. There is JJC (Joliet Junior College), Harper, COD, Oakton, then the entire CCC (chicago City Colleges) they have 2 programs at 2 different locations in the city. The CCC will give you discounted tuition if you live in the Chicago city limits, if you are out of the city - you pay more, no other restrictions that I am aware of.
All schools sort of do their own thing about lists and all that. If you have the chance and the $$ to go to a 4 year school, I would do that. A BSN is nice to have and will allow you to easily get an MSN if you want later. If you need to do it quicker, then go the associate route - either way, you end up the same - an RN and it sounds like that is your goal.
Just remember that a blocked path does not mean the end of the road, it just means that you should turn a different direction and see what other paths are there....