Not fancy and really good food is pretty much what San Franciscans go for in a restaurant. There are dozens of places like that.
As plainfood says, the places chefs go are the ones that are open late, and there aren't so many of those: Beretta, Cafe Maritime, Cav, Farmer Brown, Globe, Nopa, Oola, Thai House Express, Yuet Lee, Zuni.
If you're not terribly concerned about time, but want great food, there is also Blue Plate, it's in the outer mission. Quite a fun scene, but more food than scene by far. It's all great local, seasonal, organic, and hip.
And by not concerned about time, I mean to say that it serves till 11 on the weekends and most likely 10 on weeknights!
My friend is a chef (used to be at Zazu in Sonoma, then Market in Napa, now works the kitchen of Bounty Hunter). I know his favorite places in SF are L'Osteria del Forno, nopa and Delfina, and Ame (in ascending price/formality order).
I'm not familiar with the restaurants you mention in NYC, but if you are looking for something with great food and not loud or trendy -- because A LOT of our casual restaurants with great food are still quite trendy by SF standards -- you might check out Aziza for Moroccan.
Personally, I love Laiola, A16, Delfina, nopa, all of which are casual restaurants, but all of which are trendy by our standards... though, to be fair, SF trendy is not the same thing as Manhattan trendy -- they are sort of akin to 'Inoteca on the Lower East Side or maybe "trendy" in the way that some place like Hearth is "trendy" but also a bit younger and more casual if you can sorta imagine that.
Yes - well to clarify, we don't want UNTRENDY. We are in our 30s and still go out in Manhattan quite a bit. I just meant i don't want a restaurant that's more popular for the SCENE than for the FOOD. But definitely want a place that's lively and fun. Inoteca is exactly the right vibe!
Good! I love Inoteca... eat there often when I'm in the City.
Similar vibe with great food would be at:
A16 (Southern Italian)
Delfina (Northern Italian)
A little louder, but with similar vibe:
nopa (Modern CA)
A little more "going out" -y but with the food to back it up:
Laiola (Modern Spanish, mostly small plates)
Right vibe, haven't been since menu changed formats:
Terzo ("Pan-Mediterranean" is apparently their claim)
Either A16 or Laiola would probably be my top reccomendation. A16 just because it is unique in its sincerity about providing interesting and mosty authentic truly Southern and Sicilian dishes. It is quite dissimilar from a typical Northern Italian restaurant, and also quite dissimilar to a tomato-based one. Also, the back room (where you sit if you make a reservation) has *exactly* the vibe you are looking for, methinks. On the other hand, Laiola might be a little more of a scene than what you are ideally looking for -- the type of place where the servers are wearing old concernt t-shirts and faded jeans but the diners are maybe looking to impress on the weekends... but the food is easily the best Spanish food I've found in SF and is incredibly interesting and I find the environment very laid back, despite its more "going out" type of feel.