It is not in the immediate Concord area but may be close enough. About 40 miles south of Concord, On I-93, on the northbound side, there is a rest area at mile marker 1, just north of the MA/NH border. Overnight parking is permitted, the grounds are pleasant and the facilities are clean.
Just up the road, off Exit 1, there is a nice shopping mall. The town is Salem, NH. There is a Barnes and Noble bookstore in Salem, on State Road 28 (Broadway), that we like to visit when we are passing time in the area. Behind the store, there is a lot where a straight truck can be easily parked.
If we were spending a weekend there, and if we were not seeking tourist attractions to explore, we would probably spend the days in the bookstore or mall and the nights in the rest area.
If you are up for some tourist fun, and the weather is nice, Portsmouth, NH is a fun town in which to spend a day walking around. It has a nice waterfront park and interesting galleries and shops. When we were there, we parked on the street about a half mile from the waterfront and walked from there. Portsmouth is about 40 miles east of Concord. Of course tourist fun can probably be found in Concord too. We have yet to explore that city.