Unfortunately some of the most spectacular things to see in Banff/Jasper national parks will take you quite a distance from any full hookup campgrounds so you should allow several days to day trip so you actually see something other than a nice campground. Waterton national park is also very nice (south by the USA border) and does have a FHU campground right in town where it is easy to walk to other attractions like the boat ride down the lake.
Tunnel mtn campground in Banff is a very nice campground but it is a fair drive to see Lake Louise, Morraine lake, and Takakaw falls in Yoho national park west of Lake Louise. Lake Louise campground has power only but is much more central to the things you might want to see in the area. Others are right, Banff townsite is a zoo in summer and is really not representative of the Parks. Maybe one or two nights at Tunnel mtn to see Banff then move to Lake Louise??
Similarly it would be a shame to miss the Icefields parkway sights north from Lake louise to Jasper by whipping up the highway to get to the next FHU campground (Whistlers). I hope you can allow enough time to stop at Bow lake, at Peyto lookout, at the Icefields information center, and at Athabasca falls along the way north.
Enjoy your visit. It surely will be cheap now with the exchange rate the way it is.