We stayed in the Buckingham a couple of years ago - don't know what prices are like now - but very central. Almost opposite Carnegie Hall, one block from central park & very near Tiffany & Co - in case you're feeling extravagant!
We stayed in Affinia Gardens www.affinia.com 15 minutes walk from Central Park, 10 Minutes from Bloomingdales and a subway round the corner. It's actually an apartment hotel, we had a one bedroom with 2 huge beds and a separate sitting room and kitchen. Loads of shops, delis and restaurants nearby too.
I don't know if you have been to NY before but personally I wouldn't be too bothered about being central as it's one of the best laid out, easiest to get round city I have ever been to. We walked most places ( I came back half a stone lighter!) or got cabs, I think we only used the subway twice the week we were there.