re: Can anyone recommend an apartment complex in NOLA or surrounding area?

If you are going to Tulane med, you can stay at Papillon. If not, the Georgian is also right down the street. Both are in the lower garden district and about a 10-15 minute drive in the mornings b/c of bad traffic on St. Charles. If you're going downtown, it should probably also be 10-15 minutes.

Saulet, 920 Poydras, 200 Carondelet are other options but I think some of those are out of your price range. Saulet would definitely be affordable with a roommate though.