Carmines is more of an Italian-American-style place, heavy on the meat, cheese and red sauce served family style. It can be a lot of fun and a very good value, but I'm not sure I'd call the food particularly high quality.

Abboccato (55th between 6th and 7th) is a higher-end, excellent Italian places with much more focus on food quality rather than quantity. It's at the higher end of your budget, but shouldn't smash it too badly unless you're big drinkers.

See:
http://nymag.com/listings/restaurant/abboccato/
http://www.menupages.com/restaurantd...taurantid=5738
http://www.opentable.com/rest_profile.aspx?rid=3466

Sadly I'm not familiar with the other recommendations, but Blumie's advice is usually good for restaurants (Corpt's may be, too, but Corpt isn't a regular on this forum like Blumie).