Based on experience, will most hotels (NYC especially) hold your luggage with the bellhop for the remainder of the day you check out? I'm checking out of a hotel on a Sunday morning and need to leave my luggage while I spend the day in the city.
We've done this all over the world and never had a problem. If it's a nicer hotel, they'll probably tag it, and might charge. If it's a less expensive hotel they typically just have a room where you can leave it. Regardless, I've rarely found security to be especially tight, so I wouldn't plan to leave anything seriously valuable like a laptop. (In that case you might ask about using the hotel safe, though I've never tried. We just carry the important stuff with us.)
I do this at many hotels. It's pretty common for me to have the check out in the AM, have meetings all day, and then have a PM flight. Never had a problem. If they don't charge, I tip.