Rte 19 will not take you directly to Letchworth, but West of it. Easiest way would be 90E to 390S (Exit 46). Get off at the Mt. Morris exit (7) Tturn onto NY 408, and 0.2 miles brings you into the center of the village of Mount Morris. Turn north onto NY 36, and drive a mile to the park's northern entrance.
Or, if you want to go scenic, Get off Exit 48 (Batavia), left onto route 98 South. Left onto Main St (Route 5), keeping to the right. Follow route 63 West until route 36 (probably about 20 miles). Follow route 36 south until you hit the entrance. You'll pass within a half mile of my house on that route.