I think the lowest cost one for a full sized car was Dollar. Just remember that $5,000 was for one person doing ALL the driving. Do not even think about trying to have one of you 'sneak' behind the wheel for 'just a little while'! Each additional driver would cost around $2,000. And even at that each driver would have to provide their own insurance, either under their own auto policy, a credit card used to pay for the rental, or an auto club policy. So check with those people to see what insurance you may already have.
I will say this - New York requires that rental firms offer cars to anyone as young as 18. But the firms have good economic reasons not to and so may find all kinds of excuses not to by charging exorbitant fees, refusing to offer you insurance, refusing to allow multiple young drivers to take one-way rentals, imposing geographic restrictions, etc. I wish you the best of luck. If Dollar doesn't work out, just try each of the dozen or so major to mid-level nation-wide companies.
AZBuckk