The best bet for some running along the Hudson River in the Albany area is the 5-mile waterfront stretch of the Mohawk Hudson Hike Bike Trail. The paved, multi-use path starts steps from downtown at the riverfront Corning City Preserve, and heads north for 5 miles, paralleling I-787. There are some nice sections of the path, with water and bridge views, especially the first 2 miles passing through a couple of riverfront parks. It’s not a 100% pristine route, since the highway is right there, but it’s a good opportunity to run for up to 10 miles out and back, all off-road, with the Hudson in your view. At the northern end, you can add a ~1 mile by heading over to Schuyler Flatts Cultural Park.
It’s 1.5 miles to I-90, 4.3 miles to High St./Highway 378, and 5 miles to the end.