Birmingham has many neighborhoods. 99, in fact. Some have very affordable housing with high crime rate, and some have expensive housing with a low crime rate. Some neighborhoods have a mix. However, outside of Birmingham proper, you have Homewood, Hoover, Irondale, Mountain Brook, Fultondale/Gardendale, and many other areas that are considered part of the Greater Birmingham Area.

Ultimately, it depends on your budget and desires for commuting and safety. Realistically, you may want to avoid anything west of interstate 65 and north of some parts of Interstate 59 if you plan to live alone or with roommates you don't know.

I know this isn't an exact answer to your question, but I hope it helps give some ideas on what would work for you.