I'd think seriously about trying Priceline (PL) for a room if you want more than a cheap motel but are on a budget. Check out Bidding For Travel (BFT) to see what kind of bids are being accepted in what areas.

As for wanting to avoid traffic in LA, it's like saying you want to move to Seattle but avoid rain, or move to Miami but avoid sun.

LA is spread out; there's pretty much no way to get anywhere without driving and that means traffic.