Badaling is ok, very picturesque. It will be quite crowded if you go on a weekend but if you go on a weekday on like, a Wednesday or something, it should be manageable.
Be very very careful about "one day tours" if you have family members who are the types to partake in such things. There are some incredibly scammy Great Wall tours where they take you to some privately owned section of the wall that is basically a massive tourist trap. The biggest operator of these tours was actually arrested but I am sure there are others like it.
We took our son to Yunmengshan, near Miyun, when he was about 6 months old. Really pretty and practically deserted. The wall is crumbling in parts there and it isn't the typical pristine wall for miles and miles, but we really liked it.