I need suggestions for reasonably-priced hotels accessible to Venice Beach in a safe neighborhood. We have a vehicle so 10-15 minutes driving is not a problem. Can you help?

Define "reasonably priced". Marina del Rey and Santa Monica are both in your 10-15 minute driving window. Both are expensive. Venice isn't too cheap either, although I personally wouldn't stay in the hotels you find there.

Oh, another thing-- just out of curiosity, why is being close to Venice Beach important? There are better beaches in the LA metro area (though you DO get a better freak show in Venice)....

There's a Ramada Limited in Marina del Rey, definitely not the Ritz but close to Venice Beach....and if it's a weekend your best bet is probably something near LAX - they are usually discounted Fri Sat & Sun and is 10 min to Venice.
Hacienda Hotel at LAX is cheap all week, and decent. Maybe 15 min to Venice as it is south of the airport.

clark: LAX is a good option-- my only caveat is that traffic on Lincoln Blvd. through Playa Vista is really nasty and getting worse. Still, those LAX hotels are quite cheap and for the most part pretty nice, so....