I also used LGA. Renting a car, however, is totally unnecessary.
Directions to NYMC.
1. take the M60 bus from the LGA terminal to 125th street station in Harlem
2. take the metro north harlem line (blue) to white plains/no. white plains/valhalla, either one will work
3. taxi to school or student to pick you up if you're staying with one.
Total time is about 1.5-2 hours total, depending on traffic for the bus, and whether or not you're able to get an express train, total cost is about $10 each way to get to valhalla, plus the cab ride to the school.