The best way to get around and explore the Catskills is by car. You can enter the northeast Catskills via Exits 19 and 21 off the New York State Thruway (Interstate 87). Route 17/Interstate 86 (aka the Quickway) provides access to the southern and western Catskills. Weekenders heading north take to these highways on Friday evenings, when you can expect congestion and slower travel. The same is true heading south on Sunday, especially in the late afternoon and early evening.
The scenery is breathtaking on many of the region's roads. These include Route 23A, which, heading northwest toward Hunter, climbs steeply, passing Kaaterskill Falls; Route 10, which snakes its way across Delaware County past working farms and 19th-century homesteads; and Route 97, which runs parallel to the Delaware River.
Deer are plentiful throughout the region, so be on the lookout—especially at night. Also, be aware that cellular service in the region is spotty. In winter, snow and ice make for tough going, especially in the northern Catskills; having four-wheel drive is extremely helpful in negotiating the hilly (and often snowy and icy) terrain. In summer, slow-moving farm vehicles and animals along the roadside may impede travel; also be on the lookout for bikers and pedestrians on the road.
Note that the New York State Thruway is composed of both Interstates 90 and 87. The Thruway is the same as Interstate 87 running north to Albany, but from there the Thruway switches to Interstate 90, running west across the state. The Thruway is a toll road, so bring along change if you don't have an E-ZPass.