We found Four Mile Creek to be very convenient, an easy drive to the falls via the Robert Moses Parkway. Nice campground right on Lake Ontario. We had an electric hookup but the shared water outlets were various places spaced around the CG. Bring a copy of your dog's rabies certificate - they ask to see it.
If you camp there, you get free parking at the NF state park lots, which saves I think $10 versus commercial lots further from the falls. We arrived early and got into a very close space. From there we could walk across the Rainbow Bridge into Canada, easy customs, to see the falls from that side - viewing parks are right next to the bridge. (Or you can drive but long line of cars were waiting to cross and clear customs as we walked by them.)
Near Four Mile is Fort Niagara, a big state park also on the water, with restored buildings, nice visitor center, costumed interpreters who demonstrate musket firing, recreational areas, etc. Well worth a visit. IIRC, they have a pool people staying at Four Mile Creek can use, too.
July 4th is probably very popular so you are smart to plan early. We were there in July two years ago and it was packed.