I booked (thru Hotwire) the Holiday Inn on 57th St for my June 10th, 4 Day on the Glory. It isn't that far away from the port. However the Times Square Area isn't too far but they may not be the cheapest. Check Hotwire they had some great prices when I booked a few months ago. You may even do better than I did.
The Closest airport is LaGuardia but you might have better rates into EWR or JFK so they are worth looking into but Taxi fares will be higher depending on where you hotel is.
I have sailed on the Glory before and enjoyed it...the layout can be a bit confusing especially if you have the Aft dining room! But you will have a wonderful time!
Carnival Destiny 2011 Cozumel
RCL Monarch of the Seas 2011 Bahamas
Carnival Miracle 2010 Curacao/Aruba
Carnival Glory 2010 St. John NB Canada
Carnival Legend 2009 Western Caribbean
Carnival Spirit 2009 Alaska
Carnival Splendor 2008 Exotic Eastern Caribbean
Carnival Sensation 2008 Nassau
Carnival Inspiration 2008 Cozumel
Carnival Glory 2007 Western Caribbean
Elation 2006 Eastern Caribbean