Well, everyone is different when it comes to housing, but I only have good things to say about where I live. I work in a research lab at UAMS and I've lived at an apartment complex called Lanai Apartments for the past year. It's very close (2-3 minute drive, you could probably walk if you wanted) and the staff is friendly and the maintenance has always been very timely. They're relatively cheap (I pay 600/month plus utilities for a single where some similar places are 700+/month). Little Rock, in my opinion, is pretty expensive regardless and the rates only seem to be going up. It took me 2-3 months to get an apartment because the waiting list was quite long. Another thing to keep in mind is that they're strict about your background/renter history, so make sure you don't have bad references from previous apartments.
There's another apartment complex called Summit House that some people I work with stay at. I've heard mixed reviews about the quality, but they're comparable in distance to where I live. One good thing is that they are indoor access apartments, which is a plus for people who are worried about safety.
For me, one of the selling points of Lanai Apartments was how close they are to UAMS. The apartments are older, but they have been renovating them recently. I've never had any problems with pests, insects, etc. The air conditioner went out a few times, but they had it fixed the same day I gave them notice. I like them so much that I just signed a 12 month extension on my lease, so I thought I'd share.