Tucson Parks

1) Hiking.

For a hike with your 4-5 year old kid you can go to Ventana canyon or Sabino canyon, though the latter is more suitable for a walk with a stroller (the park has 5$ parking fee). These parks don't have playgrounds but do have scenic nature trails, so you and your kid can get quite a good workout. You can find a park near you at the map bellow.

2) Zoo.

The Tucson Zoo is simply great. It's not as big as some famous ones, like the one in San Diego, but it's very green and well planned. You have to pay to enter (membership for a family is 45$ per year, but it's totally worth it, especially if you have 2 kids), but you don't have to pay to get to a few very nice playgrounds, ponds and rose garden that are available within walking distance.

3) Mt. Lemmon.
Tucson is very fortunately located at the foot of the Catalina Mountains. In the summer, this means that you have a great place to escape to to avoid the heat. Mt. Lemmon is great for doing barbeques, hiking, and other outings with friends and your kids. In the winter, the mountains are a great place to go to for skiing or sledding fun.