There are hotels everywhere in the city now. I wouldn't stay walking distance to Broadway shows/times square- that area is awful (that said- Bryant Park hotel is a nice rec, but I figured it would he pricey).
Parker Meridian is also a spot we staycation at, mostly because it's got an incredible indoor, rooftop pool with great views. 10 blocks from shows and times square (walkalble) and close to central park. Also not my favorite neighborhood.
Subways can get you easily to timesquare from just about everywhere- so I'd agree with others to pick a more fun neighborhood downtown. My hood (lower East side/ East village) now has a million hotels, lots of restaurants and nightlife (bars, clubs, live music). But there are lots of other areas: fidi, nolita, Soho, Tribeca, Chinatown, west village, Greenwich village, meat packing, Union square, Madison square, Chelsea..etc, etc taht all have their own character and charms, and places to stay. Same goes for just across the river in places like Williamsburg Brooklyn or Long island City (queens)
I think it depends on what kind of feel you want for them right around where they'd be staying. Immediate tourist stuff, more local vibe, hipster, artsy, ethnic, etc etc.
A little more info and I can help with the hood. The people that visit will be able to advise about specific hotels better, since we only do a couple here that have pools and occasional great deals (millennium Hilton next to world trade center is the other). My mom stays regularly at a place called Incentra Village in the West village (shes there right now). More rustic and small (no elevator), and has a small kitchenette in the room.
