Anyone near new york city?? I need suggestions! :)

My husband is military and we have been denied leave multiple times. only spent 1 of our 3 years together actually WITH each other lol... we were both given 3 days off and I want to see NYC and the big tree so bad! Im so struggling on finding a good place to stay that has access to the city without breaking the bank! Any thoughts? We live near Syracuse NY. I want to take a class at body and pole if possible as well lol Thanks for any help you may have!