High Sierra Topix

I can echo some of what has been said above.

Little Lakes Valley is the most scenic and spectacular of short, easy destinations. On the other hand, getting reservations is very difficult. It is very crowded but a short ways off trail you can find some solitude. I like the north peninsula of Chicken Foot Lake, myself, as a camping destination, but others like the unnamed lakes east of Long Lake. Kids can handle it and enjoy it and adults will admire the views.

I took my kids to Round Top Lake. You can car camp at Woods Lake below and then do an overnight up to Round Top or Winnemucca Lake. You can climb Round Top while you are at it--although going all the way to the top is probably too much for small kids--getting nearly to the top for some nice views is quite reasonable. There is usually a long lasting snow bank at Winnemucca that kids like to play in.

A popular destination for first backpack trips on the Penninsula is Black Mountain backpacking camp, off of Page Mill Road just west of Palo Alto.
https://www.openspace.org/visit-a-prese ... ing-permit
It is 1.5 miles up a relatively gentle trail with views of the rolling Bay Area hills and the southern end of the Bay Area. Not as spectacular as the Sierra, but most small children don't care, they like the adventure of being out more than the scenery. We saw and heard coyotes and raccoons. Varmit boxes, running water, pit toilets, even a pay phone are available. I would say something like this would work well for a 4 year old. I took a 5 and a 2 1/2 year old there, although we carried the small one in a kid pack.

The key to dealing with kids is to realize that they really don't like the same things that we adults like. Short distances, safe water to play in, minimal bugs, small scale bouldering--these are popular. Huge scenic vistas don't seem to register on them until they get older and their sense of scale changes.

Little Lakes or May Lake in Yosemite would be perfect.

I have no idea where you are and what's close, but if you were to make it a more camping-based trip in some relatively nearby regional or state park, you can always throw a little backpack on them and hike them around in a loop or on a short in-n-out with no more pressure or impetus on them than to like it or not, and for you to find out how they're going to handle it.

Taking them out when they're so young is very cool, but it's also potentially fraught with issues that adults might only understand and appreciate when they're taking place. Best to go bite-sized, close to home, and with the ability to pull the plug quickly and bail if you have to.

If you are in northern California, the Grouse Lakes roadless area in the Tahoe National Forest off Interstate 80 is an excellent choice for backpacking with small kids. I know - I did several family trips there with my kids as young as 6 months (we carried that one while his pre-school sisters walked). There are many lakes in close proximity to each other. The area has a lot of exposed granite to give that high country feel, but it's only at 7,000 foot elevation, which avoids potential altitude sickness issues (most other Sierra areas recommended so far are in the 9,000 to 10,000 foot elevation range). Topography is mild. I'd recommend starting at the Carr Lake trailhead, about 40 minutes off I-80 (from the Hwy 20 exit, then west to Bowman Lake Road, and north on it). In just 1/2 mile, you get to long Feeley Lake where you could find some campsites along the southeastern shore - also has some sand and gravel beaches. At 1.5 miles and a couple hundred feet elevation gain, you get to Island Lake which is deeper and more alpine, with campsites on the east and west shores. There are additional lakes one or two miles further in - I like the Crooked Lakes to the north, where you can get off the trail a bit. This area is well used by both dayhikers and backpackers. It's not designated Wilderness, so no wilderness permit is needed; but you are supposed to have the California campfire permit - search online to find the site where you watch the educational video, take a little quiz, and then print out your permit, good for the whole year. Oh, and good wildflowers in mid-July.

For any Sierra area, I recommend you do the trip in August after the mosquitoes have mostly died off.

-Phil