ah, Fatburger
Not too many celebrities hanging out at the original Fatburger on La Cienega these days, Stimpy: the place closed down over a year ago. That said, it was a good burger, and other Fatburgers live on.
I second the call about the restaurant atop the Transamerica building (12th and Broadway). Used to be called the Tower restaurant, but has undergone a change in ownership, and perhaps name, since I last went. The Top of Five, atop the Bonaventure Hotel in downtown, is a revolving restaurant, but not sufficiently high to make for spectacular dining. Still, not bad.
Don't know about driving out to Rosamond if he's only here for a few days, unless cats and SR-71s are his bag. Rosamond identifies itself as "Gateway to Death Valley" and is blessed with all the charm that title implies.
Another thought, if you're heading up Santa Barbara way, is to continue on to Santa Maria and do the Foxen Canyon Wine Trail. Something like 30 wineries in the span of 15 miles along a canyon road. Turn your head and you'll miss one. Some very good wines, lots of no charge tastings, and very scenic surroundings. Of course, better to have someone else do the driving if you'll be partaking.