Best Smith Street or Court Street Restaurant
My recommendations for visiting friends from SF.
TEMPO Lovely setting, fine food, good service, nice wine list.
HENRY'S END If your friends are lovers of Wild Game. Good California Wine List
QUEEN Excellent Italian, not your neighborhood checkered tablecloth Red Sauce Italian.
PETIT MARCHE Very good solid French bourgeois home style cooking. Nice wine list.
CONVIVIUM Excellent Mediterranean Italian-Spanish, Refines cuisine, romantic charming setting, Excellent wine list.
Note that only one of these restaurants is on either Court or Smith st.
As for the topic at hand, I'd go with Saul or Grocery for high end. Lunetta for mid-level. Lucali's for casual, and Robin des Bois for atmosphere.
Though there are a couple excellent sushi places in the neighborhood, most californians would agree that even cheap sushi on the west coast matches the freshness and quality of new york's expensive joints.
Grab a bottle of wine (or 2!) off Smith & Vine's $10 table and go to Lucali's on Henry. Easily the best pizza in the neighborhood (and top 5 in NYC) and the sort of meal they won't be able to reproduce in SF.
For something fancier, I agree with Mr. Particular's recommendation to go to Grocery or Saul.
Agree with everything Oolah said about Lucali's. It's the real deal. (Their calzone is heavenly, too; there is nothing but pizza and calzone on the menu.) They were just closed for a few days for "renovations" but should be open again now. Definitely bring your wine...my recollection is that their closest liquor store is not THAT close.
Po Brooklyn (Not the kind of food I'd like to eat 3 times a week [on the rich side], but memorable. However, maybe too Italian-esque after Frankies?)
Grocery/Saul (If food quality is your #1 crtiteria, you probably stilll can't do better than these, tho it's been a while since I've been to Saul.)
Chestnut (Solid bordering on special all 3 times we went there, especially the fish. Nice vibe, too. Some have said expensive and ordinary--I don't agree, but there you have it.)
You already did Frankies--I'm afraid there's a giant drop-off after that. Really can't recommend anything.
I would recommend Good Fork in Red Hook, however, if you don't mind going a bit further afield. Interesting food, space, and location. Delicious offerings, plus the service is really nice (although I must confess the non-owner host guy was bizarrely hostile to us a few weeks back when we showed up without a reservation. It was weird, especially because everyone else in there is always super-nice, and they just started taking reservations. Maybe he had a bad day...)
You will, of course, need to make a reservation at any of these places.
re: Mr. Particular
As far as Court Street goes, there are some solid options other than Frankie's. You have Osaka and Cube 63 for sushi. I would definitely recommend Fragole, though more italian may not be what you're seeking. Also, quercy has solid french bistro food, though I think the prices are a little high and the atmosphere can be a little dreary.