Renting for less than 1 month is not a workable plan, as explained in the attached article from Frommers. You'll run afoul of New York State law at a minimum.
Be careful. You need a good NYC lawyer for any real estate transaction here, I have a list of them, just ask, as you need expert advice. Watch out that someone eager to sell--such as an owner working without a real estate agent--doesn't mislead you about what you can and cannot legally do in a particular building.
Sounds like you want a pied-a-terre that you rent out a week here, a week there, so you can stay in the pied-a-terre from time to time in between the rentals. That's a difficult plan to make work here. Most condos won't allow such renting, and I can't imagine any co-op that would even talk to you about that.
Maybe where you live in a place where people sneak around the law? But here if the neighbors complain, and we NYers are good complainers, you'll need to hire a very good, very expensive, lawyer.
Manhattan does have a few, timeshares. That might possibly make sense for you.
Otherwise you could just buy a studio pied-a-terre and enjoy it whenever you can. Apartments in top NYC neighborhoods are the blue chip stocks of real estate. Since you're not overly concerned with cash flow, you could focus on choosing an apartment with good appreciation potential.
I can help analyze any such investments, so let me know.
Licensed Real Estate Salesperson
New York, NY