Will really depend a lot on how much money you're able to spend.
But I think which neighborhood you stay in will sort of shape your opinion of Manhattan because they all have a dif feel.
Some of the cheaper hotels with deals are in the extremely manic Times Square (42nd St) area, but I'd not want to stay there. Very noisy & frenetic; even those huge high-rise hotels seem noisy & frenetic, and I don't think the rooms are nice, or so I've been told. Most tourists seem to wind up in midtown (incl Times Square) I guess because it's central & easy & there are hotel deals. But I find midtown busy & insipid & even slightly depressing. Upper East Side (where the Metropolitan Museum is) beautiful but "posh," residential & expensive. Upper West Side (Museum of National History area) is less samey & younger & lots of people love itbut also residential. But I prefer "residential" to touristy wherever I go. Chelsea is interestingit's where the Manhattan art galleries are now that SoHo has become essentially a shopping mall--but public transportation can be difficult if you're v. far west in Chelsea. SoHo, though commercialized now, is still beautiful. Ditto Greenwich Village. East Village has a bit of edge still, tho not as much as it had. Gramercy Park is beautiful and still central-is.
If it were me, it'd be downtown: anywhere from Gramercy Park downwards eg Village, Soho, NoLiTa, TriBeca. TriBeCa, where my flat is, is short short walking distance from Ground Zero & has a very dif "feel" to the rest of Manhattan--more spread out and not so high-risey and congested. So if you want a sort of urban oasis away from the the center that's it.
Think about proximity to subway--that'll make life easier. I never take taxis if I can help it; I'm spoiled I guess by the taxis in London. But there's nothing dangerous or dodgy about yellow cabs. But I love the NYC subway; I also love the buses and they're user friendly. (I think.) But walking is the best, if you have the time.
I know I haven't helped you make a decision but I hope it's helpful that I've described the dif neighbourhoods & given a few opinions.
Maybe do a search, if you can, on threads on NY--there have been lots, some with specific hotel recommendations (which i'm afraid I don't have).