You may want to go tubing on the river.

I had a look on the Park Service website. The description of the individual sites at the Upper Pines Campground indicates that this is primarily an RV campground (just 3 tent only sites if I read it correctly although obviously tents are allowed in all the sites). In my only experience attempting to camp in the valley I found that the spaces were small and the noise and congestion from the RV's prompted me to abandon the attempt. I went to a tent only Forest Service or county (I've forgotten which) camping spot just outside the park that was quiet and perfect. If a peaceful camping experience is your goal along with seeing Yosemite you might want to investigate further. I wasn't happy with the situation but I realize it might be fine with you if you don't mind lots of company. Just a heads up.

Look at the jr. ranger programs for kids.

I grew up in Calif and our family often went to Yosemite as it was nearby. There are lots of things to do in the Valley, but if you have the time, I would recommend going to upper Yosemite after your stay. Tenya Lake, Yosemite Meadows, both lovely areas and it doesn't seem so closed in. Also, you can look down on the Valley and it adds another perspective.
It looks like you are committed to camping in the valley and that's nice for an intro. There are bike paths that you can ride on and go all over the place. Horseback trail riding is an option, although in July it might be hot and dusty. There are a few lakes, small rivers you can paddle on. Bring one of those blow-up boats or a canoe to paddle around on. It's a short walk to Yosemite Falls and the rocks are fun to climb on. There are lots of granite rocks all over the valley and kids have a great time on them. The park rangers have a program going on all the time so check out their schedule when you come into the park. Take a drive to Glacier Point. That's work it. Short easy hike to Nevada Falls from Curry Village. There is a Giant Sequoia Grove near the Fresno entrance to the park and that is worth a bit of a walk to see if you haven't experienced the big trees before. At one end of the Vallery, there is the Ahwanhee Hotel. It's nice to walk around the grounds and look at the architecture of the building, perhaps have a nice lunch there one day.
Keep in mind the peak time to enjoy the Valley is May and June when there is lots of melted snow water coming over the falls. With 3 major waterfalls, Yosemite is most glorious when there is lots of water. There won't be as much in July, but it shouldn't be as dismal as it is in August.
I'd suggest bringing some binoculars to watch climbers on El Capitan, or to look at Falcons and other bird life.

Thanks so much for the suggestions! I appreciate them very much and am taking notes. So much great info. already!

We are staying in Upper Pines primarily because that is where I was able to get a reservation. My first choice was North Pines but, as many who have attempted the online reservation process will attest to, beggars can't be choosers. Still, we wanted to be on the valley floor, and we are. Close friends (who we've camped with many times) tent camped in campground last summer and had a wonderful time, so I'm sure it will be fine for us as well.

Upper Pines is fine. All the campgrounds in the valley (except maybe Camp 4) allow RVs. It will not be a peaceful, quiet, remote campground. But the kids will have a great time. There will be tons of other kids for them to play with, and you'll probably have a good time hanging out with the other parents grilling up dinner and drinking wine.

You'll be close to Happy Isles campfire ring, so definitely hit the Junior Ranger campfire talk in the early evening. A ranger gives a talk to the kids, and then they do 'smores afterwards.

Other stuff:
- Hike from Happy Isles to Vernal Falls bridge, and then up the Mist Trail to Vernal Falls, if the 4 yr old is up for it.
- Lower Yosemite Falls
- Bridalveil Falls
- Indian village and museum in Yosemite Village
- Glacier Point
- Sentinel Dome hike
- Bike around the valley and check out the meadows
- Hang out on one of the beaches on the Merced River
- Float down the Merced River (bring your own tubes, or rent tubes/boats)
- Indian Caves. It's not on the maps anymore, and the rangers won't tell you how to get there, but it's a lot of fun for the kids. It's just north of the trail between the Ahwanhee and Mirror Lake, just west of where the Mirror Lake Trail joins in. Google it.
- Various ranger talks and walks

With four days, I'd probably spend three days in the valley and one going up to Glacier Point and Sentinel Dome. It's 45 min each way to Glacier Pt, but you'll take longer to do it because you'll want to stop at Bridalveil Falls, the Tunnel View, etc. If you're coming in (or exiting) via the south entrance (Wawona), make sure you hit the giant sequoia grove right near the entrance.

I wouldn't do Tioga Rd / Olmsted Pt / Tenaya Lake / Tuolumne from the valley; it's a 90 min trip one way at least, and if you get stuck behind some timid driver in a big camper, it could take forever. Save that for another trip when you can camp up at Tuolumne Meadows.

Have fun! We go every year, sometimes twice, and the kids always have a great time.

kbob, a great summary of Yosemite options for families. We are thinking of going for just 2 days/2 nights (and we have a hotel reservation at Yosemite View, which I found from other recs here). Our kids are teens. Do you have a favorite hike or two of those you listed?

Sorry about the late response, 5alive. It probably depends a bit on how old your teens are and how active. What time of year are you going btw?

The Mist Trail from Happy Isles trailhead to the top of Vernal Falls is definitely "the" iconic hike of Yosemite Valley. It's not very long (although reasonably steep in parts). The first 2/3 of the trail are even paved! From there, if you're feeling great, continue on up to the top of Nevada Falls, and then come back down via Clark Point. This is a fabulous hike, but it's probably four to five hours or so total (from the Happy Isles trailhead). Or if you're only feeling so-so at the top of Vernal, take the trail directly up to Clark Point (for fabulous views), and then head down the pack trail from there to the Vernal bridge, and thence down to the trailhead.

The Sentinel Dome hike is really great, and quite easy. I can't remember exactly, but it's probably only one hour round trip. It's up off Glacier Point Road, so it makes sense to combine it with a trip to the Glacier Point lookout.

Or if you are hardcore (and can get the permits), do the Half Dome hike!

There are tons of other hikes; you easily find info on them online.

BTW, did you consider staying in the valley? Like perhaps at Curry or Housekeeping camp? It will take you a good thirty minutes to get from Yosemite View to the center of the valley every day, and you'll miss out on the whole early morning / evening hanging out in Yosemite thing. Like hanging out on the pizza deck at Curry having beers with other random tourists and fighting off the raccoons who are trying to steal your pizza. Or hanging on the river beach at Housekeeping camp with your neighbors watching the sunset. Or walking in Curry to get coffee at 7am and seeing a bobcat wandering amongst the tent cabins.

The valley in the summer is often sold out, but we find that you can often get spots (through cancellations) about 5-7 days before your trip.

I prefer Upper Pines to North Pines. Upper Pines, while RVs (small ones) are allowed, they are NOT the prevalent mode of transportation. Mostly families in station wagons and SUVs, almost everyone pitches tents. Upper Pines allows dogs.

While North Pines is smaller, it is also located next to the stables, and I can assure you, you can smell it before you see it! Which is why I prefer Upper Pines.

Bring bikes if you can -- you can rent, but there's nothing better than having your own bikes.

The ranger talks for kids are a lot of fun -- best ones, I think, are at Curry Village.

Also remember in summer, there's 2 pools open in the Valley -- one behind the dining room in Curry Village, or my personal favorite at Yosemite Lodge. At Yosemite Lodge, you do NOT have to be staying there to use their pool. I think it's up to $5.00/day to use the pool, and they provide towels and showers. In fact, when we camped, rather than going to Curry Village to shower, we'd go to the pool and shower there, swim, and shower again, considering it may cost you $3.00 to shower at Curry, but for an extra $2.00, you get to hang at the pool at the Lodge. There's a wading area for little kids as well as a deep end; a place right there to buy burgers and ice cream, and a view of Yosemite Falls.

kbob, thanks for helping me prioritizing. That was incredibly helpful. The kids are all in great shape and do a lot of sports, but it's a question of wise time management.

I realize we are making a compromise by not staying in the Valley. With a family of 5, we are limited to just the Yosemite View or Tenaya Lodge for availability. I wouldn't probably take the camping option this trip as we won't have room in the vehicle for extra gear.