Allardale is a nice park located on Remsen Rd. Allardale used to be farm but was then donated to become a park. There is a main trail with off shooting trails. To walk all the trails, a little over 3 miles is the distance.
Meet at the parking lot; it's located off Remsen.
Of course, leashed dogs are welcome.
Park info and a trail map can be found at www.medinacountyparks.com/pages/Allardale.html
Here is a link for the map: https://maps.google.com/maps?q=401+Remsen+Road,+Medina,+OH