Brian,
I would summarize this year's general crowd level mid-week as fairly normal for summer, with a little less pure touristy types but more crowded than normal if the hike involves list based hiking objectives that have large facebook groups, most especially the 4ks (even more than before with its 28,000 member facebook group), but the 52 with a view peaks are way, way more crowded than normal thanks to the facebook group with 4,800 members. I make the facebook connection anecdotally. I have had at least 10 people blurt out something about "facebook 52 with a view on trail" and asking me to look at their phone and their all trails app and figure out something. Also these trailheads are way overflowing. Further, even the belknaps this spring have had 60 cars in areas that used have 3 or 4 cars on a weekend just a few years ago, and even the belknaps have a facebook group with about 3,000 people. It's a different scene than a decade or two ago for sure! More kids and dogs on trails than previous years too. The key to not finding crowds is to avoid the most obvious group think routes to these peaks.
Yes, it would be a shame to let the season go by without sharing that experience with your kids. Its very easy to get sucked into the hysteria surrounding covid these days and have a limiting mindset take hold. Science seems to suggest that the risks outdoors with the wind dispersing viral load quickly would make the risk of transmission while hiking minimal, especially if you stick to lesser used trails and give it a minute after passing someone. I have been hiking with my kids.
A few comments/suggestions:
Kinsmans are very crowded from the west or east, and there have been two bear issues in that area this summer. A bear has been following hikers for miles at a time between Kinsman Pond and the Lonesome Lake trail in the col between cannonballs and cannon. There has also been some bear encounters at the Mt. Kinsman Trailhead on the west (momma and cubs).
Presi's are crazy this summer. Encountered 700 single day traversers between Adams and Jefferson between 9am and 11am one day. Unbelievable.
Anything north of the whites is faring much better crowd wise. Nash stream area was pretty quite. Percy Peak loop staying at Percy tentsite might be a good option. Even on a saturday only a few people were out there. (though it is on 52 with a view). If its been dry for a while, and you go counter clockwise on the loop its probably not too bad if your kids are experienced and comfortable on typical new england ledgy terrain. I saw a six year old on the north percy slabs. I would call it class 1 for adults, class 2 for kids. Cohos trail has no re-allowed use of their backcountry campsites now.
Rogers Ledge might be good, either the established tentsite below or at the very top there are several nice tentsites but you would have to carry water up. Looping over to Unknown Pond could be good, though both mill brook trail and unknown pond trail are usually very brushed in. But Rogers Ledge just got added to 52 with a view a few months ago so I would expect more traffic than normal.
Wild river and Speckled wilderness has been relatively quite too (other than the baldface loop). There are numerous sites on speckled, and a few nice ones a short distance down cold brook trail near the summit slightly off trail (though not sure the legality of the later sites).
Hope you can get out there!