Carmine's DOES take reservations.
www.carminesnyc.com They do not take reservations on-line, but do by phone. And yes you can order one dish and share.
Some other places to consider...you have time...explore them on-line..we have had excellent experiences and good food at all these places..When we venture in to the city, we like to try some place different each time. I tried to include in this list a variety of options...chinese, seafood, diner, barb'bque, Italian etc
Virgil's real bar'bque
Sardies
Bubba Gump Shrimp CO
Simply Pasta
Ellen's Stardust Diner
Ruby Foo's
Heartland Brewery
Frankie and Johnnies
Carnegie Deli
Simply Pasta
Manhattan Chili Co
Ruth Chris Steakhouse
and of course the ones I have mentioned before...Mars 2112, Jekyll and Hyde Club, ESPN Zone and the like, such as Planet Hollywood, Hard Rock Cafe etc
We have gone to Hershey Store, Virgin, Toys r Us (ferris wheel inside store), Disney, American Girl Store (we have a dd), FAO Schwartz, NBC studios (tours), Rockafeller Plaza, Radio City Music Hall, St. Patrick's Cathedral, Tiffanys, Cartier, Macy's Herald Square, The Plaza Hotel, Bryant Park, Central Park (zoo there) and we have even scored a photo op with the Naked Cowboy in right in Times Square...some are a little north and south of the theater district, but not too terribly far. I haven't done the Virgin Mega in DTD so I don't have anything to compare the NYC location to.
We usually drive in, park for the day, walk or take a cab as necessary. I haven't done the subway system since I was a girl..it kind of creeps me out. Grand Central has been refurbished beautifully and that may be an option instead of Penn Station. There are some nice shops, restaurants and of course the Gelato stand that was made famous by the Apprentice back when it was in it's first or second season! YUMMY!
Well, I have rambled. I hope I have helped you. Good luck and have fun..September is right around the corner. Happy Birthday too!
Michelle