In October, my fiance's parents and my parents will be meeting for the first time, the night before our wedding. We want to select a restaurant that is quiet, has good food, nice decor, and is not too crowded. Mid-priced would be preferable (say around $20 for an entree). Location in the city is flexible, but prefer not too far uptown. Type of cuisine - Continental, French, or American. Any suggestions would be great. Thanks.

Though it may be a little more expensive than you want, the place to go is One If By Land, TISB (that's the complete name. It's in Aaron Burr's former coachhouse pm Barrow Street in Greenwich Village. It's considered the most romantic restaurant in New York. It's the place that we often choose for the special occasions in our lives, and it's wonderful.
Another recommendation and one closer to your stated price(and our favorite in NYC) is Chez Josephine on 42nd Street between 9th and 10th Avenues. It's owned by two of Josephine Baker's Rainbow Children and it's wonderful. Just meeting Jean-Claude, the host and one of the owners, is an experience in itself! Marvelous food, wonderful ambiance. It's not quiet, but not raucous either.
You can't go wrong with either place. Reservations recommended for both, especially on weekends.

I agree with Howard about OIBL,TIBS. Also, Alison on Dominick is a wonderful little restaurant, as is Aureole, Cafe des Artistes, and the Manhattan Ocean Club.

Forget to mention, check Zagats NY Restaurant guide. They are also on-line at www.zagats.com.

All good recommendations, but I also recommend Capsuto Freres in Tribeca and Provence in the Village. Both French. Look all these places up on www.sidewalk.newyork.com.

I've been to Alison on Dominick and it is great and seems to fit your requirements perfectly. It is, though, a tad out of the way (not much around it).

Another recommendation is Provence in the Village. Similar cost and food, maybe a slight bit more bosterous, but it's got more going on around it.

I know this is an old post but I went to Capsuto Freres last night the food and service were excellent. After 9/11 they fed everyone for a very long time. I heard that since a lot of companies have moved they are not as busy as they used to be. I found that sad.