A lot of web 2.0 types I know love the Farmer's Daughter. Not too far from AFI (I used to spend a LOT of time there).
http://www.farmersdaughterhotel.com/ I'd say consider staying in Hollywood or West Hollywood rather than downtown -- it can make for a bit of a trip in the morning across Hollywood but it's more fun. There's a couple affordable decent places there like The Standard (if you want crazy loud and tragically hip) and a couple of Best Westerns -- one on Highland, one on the Sunset Strip -- that aren't bad at all (or weren't last I stayed there). Also, we were able to get a very affordable hookup for everyone at Next New Networks coming out for the Channel Frederator Awards at the Magic Castle, which is very close to AFI, and everyone on our team seemed to love it. If people want to band together and get a bunch of rooms there, I know a travel agent who could possibly get a discount block there. http://www.magiccastle.com/