What campground would you recommend for Grand Lake/Granby area?
Depends on whether you want amenities or not.
If you're looking for FHU, in Granby/Tabernash there's Snow Mountain Ranch at the YMCA of the Rockies. Campground is very nice.
H E R E is more info; website is a bit cumbersome, to the right on the page, for lodging type, use the drop down to choose "campground", and input your dates for consideration.
In Grand Lake, there's Elk Creek and Winding River Resort, both offering FHU sites and both highly rated for the area.
H E R E is more information on both.
If no (or limited) hookups, consider several options. There's the Timber Creek CG inside RMNP that's an excellent choice, even though it's open (trees removed due to beetle kill) with limited shade. Temps don't get overly warm there, so it's a trade off. No hookups, it's first come/first served.
There's also Arapaho Bay, Stillwater, and Green Ridge CG (USFS-Arapaho National Forest)in the area around Lake Granby/Shadow Mountain Reservoir, all highly rated and the views are simply incredible. Some sites are available with electric.
H E R E is more info on the USFS sites mentioned, and more.