So in terms of convenient hotel areas:
Grand Central (42nd and Lex) -- 4 train to Yankee Stadium, not as tourist-focused as other areas, but plenty of tourist infrastructure and easy accessibility to other areas. 7 train from Grand Central connects to LGA Q70 bus and will also take you to any number of immigrant neighborhoods in Queens filled with incredible food for your adventurous eaters.
Midtown North -- areas around 7th Ave (@53rd St) stop on the D train. More tourist-focused area with a wide variety of hotels, but right in between Central Park and Times Square, which are both areas most tourists will want to visit. E train connects to LGA Q70 bus IMO the food is more interesting along 9th and 10th Aves on the west side than farther east.
Rockefeller Center -- areas around the 47th-50th (@6th Ave) stop on the D train. Very centrally located, easy walk to east or west side, not far from Central Park or Times Square. F train connects to LGA Q70 bus.
Bryant Park -- areas around the 42nd (@6th Ave) stop on the D train. Also centrally located, a little farther from Central Park but close to everything else. F train to LGA Q70 bus plus 7 train out to those fun neighborhoods in Queens.
Herald Square -- areas around the 34th (@6th Ave) stop on the D train. This area is mainly a mid-brow shopping and commuter hub district so it's not as interesting in and of itself, but the hotels can be a little cheaper than the other areas and it's super accessible to all parts of the city. F train to LGA Q70 again.
As noted above there's also Columbus Circle -- area around the 59th (@8th AVe) stop on the D train. This is right by Central Park at the nexus of Midtown and the Upper West Side. A great area to stay in with a good variety of hotels. The one thing it lacks is an easy subway connection to the the Q70 bus. You either need to switch trains or take a train up to 125th for the M60 bus, which isn't as efficient as the Q70.