Discovery Gateway: I've never been here, so maybe someone else has some good ideas about it. Their website is www.discoverygateway.org
The Gateway fountain: if you go to the north end of the Gateway shopping center downtown their is a fun fountain that the children can play in. It was built for the 2002 olympics and is in the shape of a snowflake. Water spurts up from holes in the ground in patterns. All summer kids are there in swimming suits or just a diaper or fully clothed, running around and getting wet. Free.
Clark's Planetarium: also at The Gateway. Your kids might be a little young for the shows maybe, but they can explore and look around at the displays for free. Other things cost money. www.clarkplanetarium.org
Thanksgiving Point: This is in Lehi, off the freeway just as you pass the point of the mountain. They have a petting zoo/farm country for little kids that doesn't cost much. They have amazing gardens which you have to pay to get in, but your kids would be free. You could take a picnic, rent a golf cart, just take your stroller. They also have a dinosaur museum which is pretty good. You can buy annual passes to just the Dinosaur museum, just the farm country, or just the gardens. Or you can buy a combo pass. They have a website at www.thanksgivingpoint.com
Red Butte Gardens: This is up by the University of Utah. They have lovely gardens to walk around, play in, take a picnic. There's a fee to get in or you can buy an annual pass. The annual pass gives you discounts on concert tickets. www.redbuttegarden.org
Hogle Zoo: You could get a year's membership for just you and your husband as children under 3 are free. In addition to the animals they have a little train ride, a carousel, and a playground. www.hoglezoo.org
Tracy Aviary/Liberty Park: Liberty park has a pond where you can rent paddle boats. It also has a little carnival-like play area where you can ride a ferris wheel and other rides. There is an aviary there which costs extra to get in. They do bird shows and other fun things. www.tracyaviary.org
Sugarhouse Park: is on 1300 E 2100 S. It's just a big park with a pond where you can feed ducks and geese. A small stream feeds into the pond and kids often like to wade in it, throw rocks, etc. There are lots of covered pavillions where you can eat, or just spread a blanket under some trees. A couple of different playgrounds are also in the park.
Silver Lake up Big Cottonwood Canyon: If you drive to the very top of Big Cottonwood Canyon there's this great lake that has a boardwalk/trail all the way around it. Good place for picnic, seeing fish, walking in the woods. The boardwalk makes it really easy to take small children. You can see a few wildflowers. I've seen deer and moose there on occasion. http://climb-utah.com/WM/silver.htm
Cottonwood Heights Recreation Center: Indoor and outdoor pools, including splash zone with waterslide, zero entry, etc. They also have ice skating, fitness rooms, raquetball/walleyball courts, tennis, swimming lessons. www.cottonwoodheights.com. I know there are other rec centers in the valley, but this is the one closest to me so I know it the best. I know there's one somewhere in west valley, and another one in Sandy. Maybe someone else can give you info on those.
Public Library story time: The Salt Lake County libraries have free story times once a week, according to age. It's free but you do have to register in advance. My two year old daughter loves these. www.slco.lib.ut.us
Living Planet Aquarium: never been there yet myself, but something to look into. www.thelivingplanet.com
South Towne Center: this shoping mall has a carousel in the food court which is fun for the kiddos when I'm there doing my shopping.
Temple Square: has beautiful gardens and open courtyards, a reflection pool, and fountains. It's just a pleasant place to walk around and get some sunshine. My toddler loves going there and running from flowerbed to flowerbed. She also likes walking across the street to the north of temple square to the Conference Center and looking up at the waterfall that comes down the front of the building. www.visittemplesquare.com
This is the Place State Park: this is across the street from Hogle Zoo. I haven't been here in many years, so I'm not sure what's there to do. www.thisistheplace.org
Gardner Village: this is in South Jordan. They have a great candy store and other fun shops and a restaurant. The fun time to go there is during October when they have it decorated for Halloween. They have big mechanical witches throughout the grounds and little kids get a huge kick out of seeing. Lots of good photo opps and just a fun afternoon walking around. www.gardnervillage.com
Wheeler Farm: has petting zoo, pony rides, wagon rides. Fun for preschool age. www.wheelerfarm.com
That's all I can think of for now!