If you're looking for "cheap", then I have to assume you're leaning toward something like a state park. In PA, that means you'll be limited to electric only as far as hookups go. For a weekend, I would think you could survive with that. Here's two SP in the area you're looking at that I've camped at and recommend.
Codorus State Park
The park is located just southeast of Hanover, PA. The campground is relatively flat making it bike friendly for kids. Codorus is one of the rare PA state parks that has a swimming pool and it's in walking distance from the campground. However, if you have small children and/or need to bring a lot things with you to the pool, you might want to drive instead.
Cowans Gap State Park
If you're willing to travel a bit further west, Here's a small "compact" (only 1,085 acres) state park with everything you need for for a great time. This park is in a picturesque setting nestled in the mountains. The park is accessible from either the PA Turnpike or US-30 via PA-75. The "A" section starts out flat but becomes fairly hilly and not what I consider bike friendly. The "B" section is better but has fewer sites. You can bike (or walk) around the small (42 acre) lake with ease. The lake's beach area is sandy and has a snack bar. Below is a picture of the lake at Cowans Gap SP.
Both parks generally have good, planned, activities on weekends for "children" of all ages during the summer season. They also usually have a non-denominational church service on Sundays.
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