Freedom looks like too many choices.

So my father has a business trip to make and is not going to make it to New York after all, which means that EVERYTHING CHANGES. My mother is neither as limited in scope as my father nor as tied to canned itineraries, and so I am now open to things in a way I was not before. (It also means that anyone I meet up with will also most likely be meeting my mother, but I'm hoping this won't be a hardship for anyone.)

I have a question for my New Yorker friends, though. Staying without my father means that we are no longer limited to staying in business-class hotels, and I was thinking that I might try getting recommendations for accommodation. We do need a hotel-ish sort of thing, I think, because Mom's surgery means that she's not as up to roughing it as she might normally be. And we'd like to aim for safety. But beyond that, does anyone have any ideas? Would staying outside Manhattan be inexpensive enough to offset any inconveniences? Are there any hostels which come recommended? And so on. Any advice you can offer here, any at all, will be much appreciated.