12 & Market: Walking Distance
Just did a quick search of Open Table to see what's available then within a half mile of 12th and Market... there are some good choices. I tried to weed out the noisy ones, but my apologies if some of these are noisy and I'm not just remembering my experience to be noisy:
Farm & Fisherman
Places I've never been that might fit the bill:
Vedge (if you're willing to eat at 5pm)
Midtown Village is 2 blocks away, you have Barbuzzo, Jamonera, Zavino, Sampan, Time, Lolita, El Vez. None of them are what I'd call quiet though. A block further south and you've got Fish and Vedge, both of those are quiet. Vedge is one of my favorite places in the city right now. I had one meal at the new Fish shortly after they reopened in their current location and it was very good, I haven't been back since though so I haven't been since the recent closing/reopening turmoil there.
Chinatown is right there too.
Its Friday.... going to be packed. If quiet is the requisite.. go to Vietnam Palace.
Vedge is getting real hard to get into. I was only able to grab a last minute reservation at 5:15 for tomrrow. Really looking forward to it. I bet if you want to go there, you will be restricted to eating at the bar which is not a bad option.
I am not a big fan of Barbuzzo in the summer, especially if you are sitting at the counter, near the stove. Stiffling. And Barbuzzo is anything but quiet.