I recently cleaned up a backyard space for a client which was used primarily for the family's dog. The clients had considered using pea gravel but I suggested that play chips would be more dog friendly and lower maintenance.
In the before photo you can see the area had at one time had a few different types of groundcover including Ivy and St. Johns Wort. These are not toxic to dogs, but to simplify the 
maintenance of the area we removed everything but the large Birch tree and a few native Sword Ferns.
We then used some cardboard to further suppress any stray weeds that may want to pop through, and topped it all off with 3" of Cedar Playchips. I do not recommend the use of plastic or weed cloth in the landscape. Both of those materials do eventually fall apart, and unlike the cardboard which is broken down by worms and microrganisms, the plastic falls apart and eventually needs to be removed.
So the solution here keeps the dogs feet relatively clean even on rainy days. There is nothing to prune, mow or rake and the cedar chips should last for years. The only maintenance that they will need to do is sweep off the sidewalk occasionally.
