Hi,
Welcome to Dallas. There is a great park very close to you. It is on McKinney St. From Preston and Main, just go west on Main (not very far less than quarter mile), then take a right on McKinney. There is some construction going on there so if you miss McKinney St, go a little further and take a right on Meadow Ln, then a right on McKinney St. It is a huge park, several acres, with a wooden-fortress style playground, pavilion, and a sidewalk type walking path that is great for a stroller. My kids love it. Also, since you are new to Dallas, I highly recommend picking up a Mapsco and keeping it in your car. If you aren't familiar with Mapsco, it is a 50-page map with the entire city broken down and every street indexed. They can be found at just about any bookstore. Well worth the $15-$20.
Also, for rainy days, my kids like the little play area in Stonebriar Mall at Preston and 121.
Hope this helps.