Roughly 50 miles, probably a 75 minute drive (it's not all x-way).
Actually, if you take 19 to 19A, this will take you directly to Portageville, at the farthest southern end of Letchworth. The park is about 20 miles long.
This is where you will see the railroad bridge (park and walk out on it, it is very cool), the Upper and Middle Falls, what was once a GREAT pioneer and Indian museum that is still"OK", The Glen Iris Inn, lots of overlooks.
Leaving there by car, on the way north at the top of the hill is a pioneer cemetary that is terrific to stroll through. Mary Jemison's cabin and a statue briefly telling her story is in this area too. Back in the car, be sure to stop at Inspiration Point. You can see Middle and Upper Falls, and the bridge from there - very cool.
Heading North again go to the Lower Falls. There are steps that will take you down to the river, including a stone bridge that spans a narrow point of the gorge.
Bring a picnic lunch if it is nice: wine, beer, cheese, fresh bread, etc. The overlooks at Great Bend (highest point in the park) and near the Castile entrance are good ones. Wolf Creek is a nice lunch spot or the lawn by Tea Table Rock if it is sunny.
Now you have a longer drive to the North End of the park to see Mt. Morris Dam.
At this point if you just want to get the expressway home, take 390 north from Mt Morris to the Thruway.
PM me if you want more info.