Thanks to some misalignment in Google Maps, it took me a little bit of driving around Park West before I could find the dog park.
Located in the Mt. Pleasant Recreation Center in Park West, the dog park is a small fenced in area next to the tennis court. It's dominated by the retention pond in the center of the park, so there's not a lot of open field for dogs to run. However, if you've got a dog that loves water, that's not really going to matter much.
There are plenty of tennis balls around for dogs to run around and fetch, although most of them are in the pond so they'll need to be fished out.
One thing the dog park could use is a water hose to wash the pond water off the dogs when you're finished. There's also no water fountain for the dogs, so it's probably a good idea to bring your own water and bowl.
Here's a Google Map to the dog park.
View Park West Dog Park in a larger map