Take Rte 2 east out of Troy and head towards Petersburg.
You will cross the spectacular Petersburg Pass on the way. The Taconic Crest Trail crosses the pass there. If you head south out of the Pass, you can get to the open-topped Berlin Mt between 1 and 2 hours. If you head north, there are some nice views along the way, nice woods, and if you move along, you'll hit the side trail for Snow Hole, where there is holdover snow from last season down in the caves.
You could also drive south of Albany about 50 minutes and climb Windham High Peak, one of the Catskill 3500ers. Windham is about 6 miles r/t and around 2,000' ascent with some nice views from the summit.