Reddit reviews Saranac, Paul Smiths: Adirondack Park (National Geographic Trails Illustrated Map (746))

I would highly suggest getting a map so you can see if there are trails there or not instead of just hoping. It's hard to give advice when you're not even sure what you're trying to plan.

The National Geographic maps are the standard for the area. #746 Saranac/Paul Smiths covers the area between Lake Placid and Saranac Lake. You can see on the map there is 1 trail that covers part of the distance between Lake Placid and Saranac Lake, the Jackrabbit Ski Trail. However, since it is a ski trail, I can't vouch for it's hikability (maybe someone else here can). There would also still be road walking/running you would have to do between the two towns.

The town of Lake Placid and south of there, including the High Peaks Region is covered in map #742 Lake Placid/High Peaks

I will say there are plenty of options for other trails if you were to do more of a "basecamp" thing, especially if you're not planning to actually camp but would prefer to stay at a hotel or something in town. You could just stay town, drive to a trailhead in the morning, do your hike, and then drive back to your lodging place in town. I have done this type of trip numerous times and always enjoy it