Mammoth is pretty fun place to ride. Lot of varied options at the bike park. Most of the “lower” trails would work as XC but there are still a few that you can reach from mid-mountain or off the back side off the top if you take the gondola. Also some “off-mountain” trails like Rock Creek which is close to Crowley Lake that you can look into.
They rent bikes in the village, at the main lodge/bike park area, as well as some spots in town like at Footloose. Just depends on what you’re looking for or if any specific brands.
You can probably ride a large amount of mammoth with a hardtail-- but if you intend to ride any of the more downhill oriented trails, FS would probably be a better option.
FYI, very “unique” to ride up there with the pumice/kitty litter. Also, pretty high elevation so may take a bit to get used to it depending on where you are currently.
Also, lots of hiking/fishing/etc. to check out w/ the family. Depending on how long you have, also may be worth a day trip to Yosemite-- just would need to look into the potential permits again this year due to Covid.