I usually keep a couple ant traps in the camper (we don't store food in there) in the storage bins. There's been a couple camp sites we've been at that I see the little buggers on the side of the camper. I kill what I can see but am always worried about the ones that got into the camper that I didn't see. So before I take it back to storage, I make sure the traps are still good, or replace with new.
I store my camper on my sisters property so it's on the grass. The landscapers mow the grass, but obviously can't get under the camper. So every couple months starting in spring, I sprinkle some bug granules on the ground where the camper sits. Helps kill the ticks, earwigs, etc. that might be near.
Never really worried about mosquito's. We usually use bug spray for us, the dog, and for the little kids, my mother in law got us some of these cool citranella patches that we can put on their clothes. I've used them before and they work quite well. You don't go to be smelling of citranella or feel like you have a bug spray glaze on.
The only problem I have had is ants last summer, they had some South American ants infesting the forest areas in SC. They came out and sprayed the campsites daily. The ranger was very good about making sure he got all areas of contact with the ground. We found ants inside one morning. Finally traced them to a branch that was hitting the top of our awning when the wind would blow. Now how did those ants figure out the occasional touch of a tree branch to a piece of awning would eventually lead them to food? Lost half a chocolate cake to those buggers!