Eva, The Cloisters is way, way uptown. Far. A very long cab ride. Also there's the issue of your getting back. Not sure that cabs are readily available up there. I can't remember where I saw four in a cab. Not a good idea.
The problem with the subways is the stairs. Lots and lots of stairs. However, I believe that there's an elevator in the station by the Cloisters. However, there probably won't be one in the station when you're coming back from the Cloisters.
Joe is much more familiar with the neighborhood and knows about the comings and goings much better than I do.
Plus I haven't been on the subway in a long time. Can't do the stairs.
BTW, the Cloisters is west.
Another thing to know. New Yorkers are very slow to accept name changes. Sixth Avenue was renamed Avenue of the Americas decades ago. Find me a New Yorker who calls it that. Somewhere there must be one. I used to work on Sixth Avenue and would often encounter tourists who had walked from Fifth to Seventh and back again. Where's Sixth? The city now has two street signs.
The 59th Street Bridge was recently renamed the Ed Koch Bridge. I think. I'll be dead long before anybody calls it that.
Two more things just popped into my head. Broadway starts out west and eventually goes east. It's not parallel to the other streets. So depending on where you are, Broadway is either east or west.
Last, the north-south streets are short. Easy. The crosstown (east-west) streets are l-o-n-g. I mean L-O-N-G. For a walking-challenged person, this is important to know.
I'm rambling. Sorry.