I used to live in Avalon Fairway Hills. The apartments are older but kept in good condition (in my experience). The 1BRs with a den would be at the top of your budget, but I had no major complaints when living there. I think because the apartments were older, I hardly ever heard my neighbors. It's pretty close to downtown Columbia and right next to a highway exit, so pretty convenient location.

Anti-recommendation: Definitely don't go to Paragon Columbia (the apartments immediately next to Costco). They're way overpriced and my experience there was pretty miserable.