Dream Lake is perfect for what you're looking for, and it's one of the classic views in the park. It's also the one hike that you'll see half the people in the park.
Gem Lake is also a decent distance, though it's a bit steeper and not quite as scenic. It will however, be much less people to deal with.
Drive to the top of trail ridge road and the visitors center - if you can find parking, get out and have the kids run up to the top of the hill next to the parking lot. It'll be over 12,000 feet if I remember correctly. (if you do the next paragraph, you'll have to go through this parking lot as well on the way out)
Take Fall River Road (it's a dirt road with some holes, but doable in a regular passenger car - probably not an RV or overly long vehicle though) to near the top. There's a wood fence on the right side of the road and area to park. There are a couple of places to hike to, one is a very short hike, the other is longer and at altitude, but it goes up to Marmot Point, which is a fantastic view. (and you're almost guaranteed to see Marmots)
Bierstadt Lake is another short-ish hike. It's pretty steep until you get up in the forest where it levels out for the last little bit to get to the lake. Beautiful views of Hallett Peak from there.
On the west side, there's East Inlet at the edge of the town of Grand lake. It's a short hike to Adams Falls where most people hike. (a la Dream Lake) Past the falls sees less people. There's a great chance to see moose here, though keep your distance if you do. They're big, quicker than they look and ornery. Keep your distance and a tree between you and the animal if at all possible. There's a beautiful meadow about a mile or so in with great views.
