I actually stayed there a few weeks ago, there is a 24hr gym but we only used the hotel as a base and take note although there is a starbucks in the bar you can only get take out to your room untill 11 am. Grand central is less than 2 min walk form the hotel and has plenty of food places there, you are also only 10 mins from time sq and rocafella cantre so you must go to the vewing platform top of the rock for the best ever view of the city. they dont seem to have pay per view movies in the rooms either, its good as a base but would suggest if your not going out then take a book or something
Based on the site, there isn t anything to do except the pool and if you re going any time soon, it will be too cold. There is a bar and restaurant and some sort of lounge/bar but you didn t say how old everyone. There is also a fitness center.http://www.theroosevelthotel.com/About/
Venture outside. You are across the street from Grand Central Terminal., within a good walk of the Empire State Building, Timew Square, MOMA, and many other sites and attractions.