Fastest routes, completely avoiding NYC:

From Lancaster, take PA-72 north to I-81 to Scranton, then take I-84 to I-691 to I-91 to Rocky Hill. Should take about 6 hours and it's quite scenic.

Adirondack Park is huge, so I'll get you to Saratoga Springs. Take I-91 north to Springfield, then I-90 to Albany, then I-87 north. Rocky Hill to Saratoga Springs via those routes is about 2.5 hours.

From Watertown to Niagara Falls, stay on the US side - I-81 to I-90, about 4 hours. Going via Canada adds about an hour and a half and puts you right through the middle of Toronto.