As long as you're not planning on driving to UCLA from there, I think you should fine. The traffic can be pretty bad during rush hours.
Some of my friends lived in the Promenade Towers... the rooms are decent at best for LA standards. If you're used to the old buildings out on the east coast, you might actually find the Promenade to be nice.
The area is not terrific... downtown LA is not exactly the most convenient place to live. However, if you're talking about going to USC or something else around that area, downtown is probably your best bet.