A few options to consider (I would choose option 2 - I have stayed all the options below)
1) ALoft in Harlem about 10 minutes walk to Columbia and they have paid parking
2) or Just stay mid-town, for example, Westin next to Grand Station. You have to pay for parking around the hotel, but it is easier to find reasonable parking and a lot of food options there.
3) To leave the crowded city and be economical, you can stay at Sheraton Lincoln Harbor Hotel next to Lincoln Tunnel, they have a shuttle taking you to Time Square. This might be the only option with free parking.
4) Westin/Marriot/Double Tree next to Holland tunnel, you have to take PATH to go to Manhattan. Parking is not free, but not that bad.
Option 3 and 4 have the best view of Manhattan skyline
