If you don’t mean kids school summer hols, Center Parcs isn’t bad for 4 night stay early June. Longleat is a great base for road cycling, they do e-bike hybrid hire now that you can take off campus, you would have to bring your own nice road bike and store it overnight in the villa storage cupboard just inside the villa door.
There’s also an MTB park (Windhill?) on Longleat estate, plus a fair few bridal paths to explore in the area.
If you’re feeling adventerous, instead of sticking to the numerous hills close to Longleat, you could make a day of it by doing a handful of the Mendips hills including Draycott Steep; Cheddar Gorge; Burrington Coombe; Old Bristol Rd etc. in a ~75 mile loop. Did a variation on this in Nov ’17 on my 29ered fatbike equipped with 2.35″ G One Speeds on the first day of our stay, having got train to Warminster at ~1000 and meeting everyone at the villa around 1700 after having fun with my navigation with offline maps back then.