there is one near US embassy at libertador y sarmiento. there is also one in Plaza armenia (armenia y costa rica). these are all small circular enclosed spaces. I find they are not the best places to socialize pups. they aren't the best spaces and tend to be not very clean for you or the dog. if anything happens it will also take you some time to react.
Buy an extendable lead and go to the palermo parks (same one near embassy). in my experience it is a great place to meet other dogs and still have control over yours.
ps,. the mornings are usually taken over by the actual dog walkers with their dogs. again, it's a good start to walk by and slowly introduce your dog to theirs. if it's too-much too fast, then go in the afternoons when it's just owners.