Huckleberry Rail Trail (nature trails in town, walking distance from the house. the closest access point to the trail is in the Rip Van Winkle Park, by the playground)
Huckleberry Point - 4.5 miles, stunning view
Dibble's Quarry - the link is for the Pecoy Notch trail, but if you just go to Dibble's Quarry it's about 45 minutes each way, and it's a favorite spot to sit and watch the world, stunning views.
Indian Head Mountain - this route along Jimmy Dolan Notch clocks in at just under 5 miles, but you could combine it with Twin for something longer
Twin Mountain - again, you could combine with Indian Head, or Sugarloaf for something longer
Blackhead and Black Dome Mountain (and throw in Thomas Cole if you're feeling extra ambitious)
Hunter Mountain via Becker Hollow (technically this one is under 5 miles but it's aggressively uphill, so I'm putting it into the over 5 miles category!)