Oh my, there are a ton!
A short brief:
Renaissance is close with a shuttle, but off the main street (Century Blvd.)
Doubletree is farther from the airport, don't know about shuttle, and should be relatively quiet.

I suggest you go to the hotel forums, pick your favorite chain or where you have status/points, and do a search on "LAX" "Los Angeles airport" or similar; you'll get a ton of hits.

-dp