We have stayed at the Lodgepole Campground for the past five years. All of our campsites have been in the same loop up near the waterfall.
We have been during June and July in previous years and choose August this year so that we could splash around a little in the river. Last year they had a really high water flow at the end of June and we were not able to slash around since the water was to rough. There is a nice small pool at the bottom of the campground waterfall (the Topeka Waterfall is about 2 miles upstream) and a smaller sitting pool that has been carved by the river above that.
The water is not too cold and the surrounding rocks are warm after a day in the sun. It makes a wonderful place to splash around after a day of hiking.
The tent only campsites that we enjoy are in the Upper Lodgepole loop. Sites 124,125,126,128 are all riverfront property. During the high water season 128 has a small private stream that runs near it. This year we were at 128. The website that the National Park Service uses to book the sites (recreation.gov) has a map of the campsites. They are all close enough, but not too close to the bathrooms which are located directly across the lightly traveled road. There is a water spigot right behind 124. Site 128 is the most private of the four sites that we like. It is also farthest away from your car and 15 steps up. Not too bad, but on your first day at elevation hauling all of that stuff can be a chore. Site 128, being up the hill a little has no close neighbors and a fallen tree provides more privacy. There are two sites on that loop (123,127) that offer little privacy that I don't recommend if you can get on of the others.
If you have a large tent site 124 would be a good choice. Our tent hung off of the tent pad at site 128 (lined with rocks) and was a little bumpy. The tent pad at 124 is huge. Sites 124 and 128 also remove your tent from the fire pit so you don't get smoke wafting in the tent all night long. Site 128 is the largest of the four sites.
The Lodgepole Market just down the hill has ice, snacks and so far everything that we have forgotten we have found there. There is a mercifully small amount of souvenirs for our three kids to choose from. You can also find a burger, sandwiches, laundry and a hot shower near the Market. The Visitor Center with tickets to Crystal Cave (you should see it once) is a short walk away.
Sequoia National Park has just implemented a Shuttle route to a few stops this year. There are two stops in the Lodgepole area that take you as far as Crescent Meadow. We were able to do a couple of point to point hikes (instead of round trip) using the Shuttle stops.