Generally, though almost no restaurants outright ban children and therefore noise is always possible, the higher the menu prices generally the quieter the atmosphere. As a solo adult traveler, or one who travels with other like-minded adults, my favorite dining locations include:
Jiko, California Grill, Narcoosee's, Yachtsman Steakhouse, Le Cellier, San Angel Inn, Nine Dragons, and Turf Club. Other places I'll visit that have kids and families, but tend not to be as manic and crazy as the character and budget spots, include Kona Cafe, Grand Floridian Cafe, Teppan Edo, Hacienda de San Angel, and Brown Derby. A favorite of old was Coronado's Maya Grill, but it was utterly ruined a year or two ago, and went from high end unique latin/Mexican fusion steakhouse to generic family restaurant space. As for entertainment while eating, that's a tougher call - haven't really come upon one of those yet. We generally do dinners at a good restaurant, then go hit a cool spot for nighttime entertainment afterwards...rarely do we attempt to combine the two. Favorite night spots are French Quarter's blues/jazz club, House of Blues back patio, Raglan Road, Jelly Rolls, or just strolling Downtown or the parks.