I would highly recommend the 2 Frick OLEAs (off-leash exercise areas) that menge101 linked to.
Many many people do not follow the leash rules in Frick park which ruins it for those of us that have older dogs that don’t want young dogs running up on them; and as a result are seen as “not friendly”.
They are both fully fenced with 5-6ft chain link and have air-lock style entries to reduce the risk of off-leash dogs running out when someone enters/exits.
They both have benches for patrons to sit on/at and a few things for the dogs to play in/on/around. Obviously you will have a mixed bag of people and dog types using the OLEA, so your mileage may vary but you run the chance of seeing annoying/aggressive dogs and inattentive and/or jerkish owners at any dog park.
I would only recommend Hot Dog Dam if the dogs you are sitting for have a good recall as that OLEA is not fully fenced in (I haven’t been there in a few years, so hopefully this has been fixed). The dog area is/was separated from the jogging trail by a split-rail fence and chain link, but the hill on the far side of the eponymous Hot Dog Dam is not fenced off at all and leads right up to a highly traveled road and intersection (Forbes and Braddock Avenues).
That being said, this OLEA is awesome for dogs that love playing/jumping into water or need a bit of a cool down or non-soapy rinse off from other activities.