Almost all of the high-end restaurants are relatively quiet, including the super-expensive temples of haute cuisine (Alinea, Grace, TRU, Everest, Sixteen), and the next tier of somewhat-expensive restaurants (Naha, North Pond, Acadia, Michael, the Lobby, Oceanique, Quince). However, because they are at least somewhat expensive, they're not places most of us would go on a regular basis.
When you start looking at moderately-priced restaurants with creative/delicious food, the problem is that for those very reasons they tend to be pretty darn popular, and even the ones that don't approach ear-splitting levels are still pretty darn noisy. When I think back at moderately-priced restaurants I really enjoyed this year, they were all rather noisy, including places that are among my favorites where I keep going back (Deleece, Sable, GT Fish, Campagnola, Frontera, Salsa 17, Inovasi, Abigail's, E+O) as well as places I was trying for the first time (La Sirena Clandestina, Salero, Kinmont, Yusho, Carnivale, the Bristol, Boltwood, Fish Bar, County Barbeque, Quartino). So I wouldn't recommend any of these to someone looking for a quiet restaurant. The only mid-priced places that come to mind as being not so noisy are two places I didn't hit this year: Atwood and Café des Architectes. So those might be two candidates for you.
Other than that, I'd suggest dining at off hours, either early (seatings of 5:30 or before) or late (seatings 9:00 or later); that way, a place might be noisy for part of your dinner, but part may be relatively quiet. Similarly, weekdays tend to be less noisy than weekends, at least at places that aren't totally full during the week. If weekday lunch works for you, that's another possibility for some places that might be quiet; for example, Naha offers a three-course prix fixe for $26.
Incidentally, in their user reviews, Opentable shows summary ratings for "noise level". Unfortunately, there's no way to sort or filter on this characteristic, so you would need to look up each restaurant individually to find which ones have the less "energetic" noise ratings.