I don't get down to the city very much but if you like museums the Museum of Natural History and the Metropolitan Museum of Art are definitely worth the visit. The Met has a complete Egyptian tomb on display. Either one could take a full day and you still won't see it all.
If you have the time and the $$ try to see a show! Nothing quite like Broadway and so many good shows. Often you can go to Times Square and get a matinee ticket for a bargain price.
The best known quilt shop in the city was City Quilter but they have closed. Some people say to go to the garment district in Manhattan but then you will be exposed to all kinds of fabrics, mostly for garments so you would have to sort through to find 100% quilting cottons. I have never been so can't say.