Your best is to stay in a hotel near the UAlbany campus (on Western Avenue or Washington Avenue by The Northway [I87]) or in one of the many hotels along Wolf Road.
These hotels are all about 25 minutes from the park.

Some options:

Best Western Sovereign Hotel
1228 Western Ave Albany, NY 12203
(518) 489-2981

Fairfield Inn - Marriott
1383 Washington Ave, Albany, NY 12203
(518) 435-1800

Holiday Inn Express
1442 Western Ave Albany, NY 12203
(518) 438-0001