State parks are usually the easy yes for a dog, which is exactly why the strict ones catch people off guard. These popular parks either ban dogs outright or keep them off the main attraction.
Some are nature preserves that protect fragile ground, like Walden Pond or Radnor Lake. Others limit dogs to certain trails or close the beach in summer. Each page has the specifics.
None of this means skipping the trip. It just means knowing before you go, and having a backup nearby.
For the parks near these that do welcome a dog, your state guide has the full list.
Usually because they protect a fragile or rare habitat, a nature preserve, or a sensitive shoreline. These total bans are the exception, not the rule, for state parks.
Most often it means dogs are welcome on the trails but banned from the swimming beach, or kept off one signature trail, or restricted seasonally. Check the park's page for the exact area.