If you're talking $20/entree, then I'll assume you're also talking about $50/person. (Alcohol would be the big variable here. One glass ea. vs. buying a med. priced bottle, vs. several coctails and/or after dinner drinks, etc.)
That said, and taking your stated parameters into account, the next question would be ambience. Do you require dim lights, linen, and quiet, or would you be just as happy with a bit of crowding and celebratory bustle going on around you?
For an upscale American /intimate/neighborhood feel I would say check out
Magnolia Cafe (on Wilson in Uptown, or
Tweet on Sheridan). Both can be a bit crowded, but have good kitchens.
We had a really lovely meal at
Le Bouchon on prix fixe, Tues. I think the regular menu would still be in your range.
There have also been some really wonderful sounding posts about
Sweets and Savories, though it might push your price point and I haven't been there.
Have also heard (but not had) good things about the new tapas place,
Rioja on Clark in Andersonville. Other places I've heard first-hand good things about are:
Thyme Cafe, D'Vine, Tizi Melloul. All very different.
Mon Ami Gabi also has its fans for classic med.-scale French. All worth doing a little research on yourself, since these are 2nd hand impressions.
Just some scattered impressions. I'm sure there are many great candidates out there.
"Strange how potent cheap music is."