I've been there but haven't stayed there - you don't have to 'stay' there, it's just a part of town easily accessible from other parts of town. It's like saying you want to see the museums of South Kensington: you can stay anywhere in London and get there quickly if you want. (I remember one night we went to see Stomp there years ago, then hopped on a bus to get back to our hotel off Times Square.) Sorry I don't have any local accommodation advice.
I have stayed at The New Yorker a few times and can deffo recommend it (481 Eighth Ave, 34th St & 8th Ave)- However it is more central and not in the Greenwich Village area...but you will find a link to reviews here
http://www.tripadviso...rk_City_New_York.html