The Hudson Valley can be a paradise for dogs, if you know where to look. Let me start off by saying, the official rules for a lot of parks call for dogs to be on leashes at all times. This is for the safety of all guests, as well as dogs. However, if your dog is well trained and capable of being off leash without causing issues, there are plenty of open spaces for them to roam.
I can't stress this enough, IF YOUR DOG IS NOT CAPABLE OF BEING OBEDIENT OFF LEASH, PLEASE DO NOT RUIN IT FOR THE REST OF US!!!
Now, for the fun part...
1) Drayton Grant Park aka Burger Hill (Rhinebeck)
Dogs are always welcome, but the park can get very crowded, so please keep all dogs on a leash unless you have the park to yourself. You can't see the top of the park from the parking area, so please don't let your dogs roam free until you've made it to the main hill.
It's a quick 5-10 minute walk to the top of Burger Hill, which offers one of the most breath taking views over Rhinebeck. There's also a cool metal relief that identifies all the mountains that you can see. You can get a full run down of Burger Hill here.
2) Poet's Walk (Rhinebeck/Red Hook)
Located off River Road and steeped in American history, Poet's Walk encompasses over 120 acres of open space. Local legend says it was named Poet's Walk in honor of Washington Irving and Fitz-Greene Halleck, who were known to stroll the park in their time. Filled with rambling hills and amazing vistas, it's best to take your time and casually stroll through the meandering paths that dot the landscape. It's hard not to be in when you gaze over the Hudson from Overlook Pavilion.
For a full history of the park, check out this and this – if you're a history buff like me, learning the back story of this gorgeous park is almost as thrilling as experiencing it for the first time!