Wild Goose Chase- dog-friendly venues nearby?

DH, Dog, and I currently have a room reserved at a pet-friendly inn for the Wild Goose Chase in Cambridge, MD. But, with the recent news that we will both be taking pay cuts in the near future, we are considering making this a less-expensive day trip for the three of us.

So, are there any dog-friendly parks (need not be off-leash) or other similar venues nearby where DH and Dog can hang out while I'm off riding my bike? A quick google search didn't turn up much, and there do not appear to be any state parks nearby.

Thanks in advance for your help!

GENERAL INFO & QUESTIONS
info@ci.cambridge.md.us

They might know but it doesn't look promising. I looked for the parks department on the city website but they don't have one.