We just came back from spending a couple of nights at this campground.
. We stayed in a cabin, but they seemed to have a variety of trailer sites. Very quiet, clean, lot's to do, very close to Niagara Falls (15 min. max). It might seem a little pricey for what you are looking for. We have lot's of kids, so the ammenities are what we wanted (pool, mini~golf, kayaking, zip line, crafts, etc.). This is it's second year being open, so everything is pretty new.
There is also a KOA on Grand Island. The zip is 14072. I've never stayed there, but I've read it's much nicer than the KOA that's listed closer to Niagara Falls on the KOA website.
There is a $1 toll to get onto Grand Island, so the back and forth may deter you. It's right between Buffalo and Niagara Falls, so very central without being in the "City".
I only live 4 minutes from this campground, so if you have any questions, please lmk.
Hope that helps!