Sasquatch Provincial Park has two camp site areas. It is just to the east of Harrison Lake which is east of Chilliwack a short distance. I believe there may be a bit of gravel road into the area.
Heading the other direction, west, there is Porteau cove as someone mentioned between Vancouver and Squamish. Just past Squamish a few kms is Alice Lake Provincial park. Some sites there have electric hookups and the park has shower facilities. There is another private camp site south of Whislter on Highway 99 near Brandywine Falls called Whistler RV Park & Campground. I have not been in there but it is relatively new place. Whistler has a camp site called Riverside Resort.
Lots of great hiking and mountains in the Whistler area. Whistler would be about 200 km from Chilliwack.
A drive up the Fraser Canyon east of Chilliwack is a beautiful area. There is a provincial camp site in the canyon called Skihist. Can be hot and dry there in the summer.
Here is a link to the BC Provincial camp sites.
Visiting Parks - BC Parks - Province of British Columbia
There are a lot of very nice places within a relatively short drive from Chilliwack.