OK lets see....Taxi from SI Ferry back to times square will run you approx $35 dollars i think. With a wheelchair you might need a special cab.

Weather is cold, highs below 30. bundle up.

Museum - I would stick to Moma, Guggenheim, or Metropolitan Museum of Art. With that schedule I would pretty much skip the West Side (Museum of Natural History)

The route I would recommend is for you to go up 7th Ave, enter Central Park, stroll around up until 70th St or so, swing to the East Side, around the Central Park Zoo. If you so wish, you might catch the Wollman ice skating rink.

I'd go to FAO Schwartz, maybe the Apple store, though that may be nothing special, walk down Fifth Avenue (Might want to try the Sony Tech Lab) by Tiffany, Saks Fifth, Rockefeller, the big cathedral, down to 42nd St where you run into Bryant Park and NY Public Library.

That's probably two hours.

You can diverge right (East again) down 42nd two blocks for Grand Central. Or...continue south on 5th Ave for Empire State Building. Hopping back to Times Square should be no problem from either of those. I hear the Top of the Rock at Rockefeller is better than Empire State though.

As for a Southern route, there's less there. I would start at Winter Garden near the World Trade, walk down towards the SI Ferry. You'll pass the Jewish Heritage museum on the way. You can see Ground Zero from the Winter Garden. Wall Street is not much to see in my opinion, but if you want to see the bull, then turn inland a bit, takes you away from the river and a nice view of NJ. You can see lady liberty from there. I would try to catch the South Street Seaport, which is a bit north of the ferry, on the East Side.

The SI Ferry is about 20-25 mins each way. You can make a round trip in an hour.

As for which museum to recommend, depends on your interest

Enjoy NY!