Henderson Beach State Park (https://www.floridastateparks.org/
), in Destin, is wonderful! That would be my number one destination (we go there quite often we love it so much). Great beach, many pull-through sites, vegetation separating sites, mostly large sites, etc. Not full hook-up,. though. Only costs about $30 a night. Lots of things to do in the Destin area (restaurants, shopping, site seeing, etc.).
Their sister park (free admission to this park with your Henderson Beach tag) is Fred Gannon Rocky Bayou State Park in Niceville. Fred Gannon is about 10 miles north and has a lot more activities than Henderson Beach. They have quite a few trails, Bayou kayaking, nature demonstrations, etc. This would also be a good alternative to the beach-side campgrounds as it is very inexpensive (around $18-20 per night) and you get free admission to Henderson Beach beach when staying here.
Top Sail is near here, also. Top Sail is a little more expensive than Henderson Beach (depending on the site and location) at about $50 per night.
Emerald Beach RV Park (https://www.emeraldbeachrvpark.com/
) in Navarre is very good. The sites are close, but it is still nice. You still have some room between the RVs. The location is right on the Sound, so the view is fantastic. Navarre Beach is just over the bridge and is one of our favorite beaches in FL. Again, plenty to do around here. Pensacola is about 15 minutes from here. Rates here are about $55-60 per night depending on if you want a beach-front site or not.
Personally, I would steer clear of Big Lagoon. Very narrow road, very tight sites, weird neighbors, a long way to restaurants, muddy sites, etc. We used to go there, until we found many better places to go.