Lum's Pond is quite far from St. Michaels.
As mentioned already, Martinak State Park, MD is also close to St. Michael's.
Tuckahoe is probably a tiny bit closer to St. Michael's (compared to Martinak) and has the most "private" campsite areas of the three. The sites are pretty well separated and most have brush around them.
Tuckahoe also has a nice frisbee golf course. Make sure you bring some frisbees as the teens can spend some quality time there arguing over the rules while they play. Or maybe Dad can show them how it's done.
Tuckahoe has a nice little lake with boat ramp (electric motors only) and waterfront area that is a 3 mile drive or one mile hike through the woods to get to. Very peaceful place - both the campsites and the day-use area at the lake.
Tuckahoe also has an adventure area including some high ropes and a zip line at the far end of the group campsites - but I don't know how often it is open. The ropes area is pretty well hidden - it is near the non-electric loop in Tuckahoe, across the field where the group campers park.
Martinak is nice also and is popular with motor boaters and fishermen as they can use the boat ramp right in the park to put into the tidal river - just a short walk from the campsites. The campsites at Martinak are a little closer together than at Tuckahoe and the underbrush is not as dense so not as much privacy between sites.
Both Martinak and Tuckahoe are wooded campsites. The underbrush at Tuckahoe is denser so it has a little more secluded and private feeling.
You can probably tell I like Tuckahoe better. It is my favorite local campground that I camp at 2 or 3 times each year. But I sometimes go to Martinak if Tuckahoe is not available.
If you are into small boats, you might enjoy Martinak better as you can walk to the boat ramp and watch the entertainment. Lots of local people and campers put their boats in there. The river there is tidal, wide and navigable for miles - all the way to the Chesapeake Bay and Atlantic Ocean probably.
Ed