Very late date to find open sites but I will give you some possibilities below:
The National Coast Guard Festival that's in Grand Haven each year begins this year on July 26th and there will be a couple hundred thousand people in town for the next 10 days. You will be around just before this. It's been going on for the last 88 years and the city is well setup for the crowds and handles them very well. Here's the link:
http://www.coastguardfest.org/
Grand Haven/Spring Lake etc is approx 5 miles south of Hoffmaster S.P. depending on which road you take. Hoffmaster State Park is huge and has very tall sandunes and 2-1/2 miles of pristine Lake Michigan sand beach with lots of trails. We camp there usually every year.
Much depends on what you and/or your kids like to do and if you are on a very tight budget or not. There's more to do than you could if you were camped around here all summer long.
http://www.visitgrandhaven.com/camping--rv-parks-101/
8 CG's on this site and I'll list some more.
Lake Michigan RV Resort 6 miles south of Grand Haven just off US-31. I have 2 ph nos. for the resort 616-842-9395 and 616-850-8530 I haven't been in the CG for several years but it used to be rated the "Best" Yogi Bear resort in the USA. The original owners have retired and it was sold a few years ago.
River Pines RV Park/Campground 616-895-6601 It's roughly 6 miles east of downtown Grand Haven on the south side of the Grand River.
Conestoga Campground 616-837-6323 It's on the north side of the Grand River and has a boat launch. About 6 miles east of Spring Lake, MI
I don't care for Camper's Paradise because it's right next the busy US-31 4 lane divided highway but it is close to everything. Just south of the city limits road.
North of Muskegon is the big "Michigan's Adventure" Amusment Park and Water Park. Largest in the state. $
There's a WWII submarine in the water in Muskegon you can go down into and explore. $
Lots of programs at Hoffmaster SP Gillete Visitor Center - free
A mall and a gobs of other stores just east of US-31 between Muskegon and Grand Haven.
Concerts in Central Park in Grand Haven on Tuesday nights. Various type bands etc. free
Big Band Dances at the waterfront stadium in downtown Grand Haven on Wednesdays $3/person, I think
Concerts at Mill Point Park in Spring Lake on Thursday nights. free
A many mile long wide Boardwalk along the Grand River in Grand Haven from the end of the 1/4 mile long pier out in Lake Michigan past downtown .7 miles and on past marinas and water front stores etc and the charter fishing fleet all the thru into Spring Lake. Extremely popular and millions walk it every year. Lots of boats, benches with backs, bathrooms, food and/or snacks/ice cream along the way including the Coast Guard buildings and basin. Plenty of outdoor cafes downtown. Downtown is extremely clean and beautiful. Over 90 eating places in the local area if so desired.
A very nice skateboard park, water park activated by motion, and nearly 200 miles on paved off street bike trails to ride.
Many beach volleyball nets at GH SP.
Fishing, open air trolley car rides - cheap, Wind Dancer Schooner Charters for families $
Several museums to visit. free
Just the tip of the iceberg but may give you some ideas. We've lived here for over 70 years and know what it's like.
So much to do and so little time and you'll be back again like the millions of others do again and again!
A superb CC LB 4X4, GM HD Diesel, airbags, Rancho's, lots more
Lance Legend TC 11' 4", loaded including 3400 PP generator and my deluxe 2' X 7' rear porch
29 ft Carriage Carri-lite 5'er - a specially built gem
A like new '07 Sunline Solaris 26' TT