I read good things in earlier posts and I'm happy to report that the wife and I had an excellent meal at Giovanni's (Venice Blvd and Clarington):
Rolled eggplant, ricotta, pine nut appetizer
Lasagna (I believe the noodles were fresh, so velvety)
An incredible custard tart with chocolate and pine nuts
The whole meal was just north of $30, with beverages. Too bad it's located in a little dumpy mini-mall, like half of all businesses in LA, but it's a fantastic neighborhood restaurant. We had a great chat with the Italian owner. Next time we'll bring our own wine and pay the $3 corkage (no license).