We BP a fair bit with our 7 + 11 year olds. Unlike my childhood trips in CA, there's no predicting summer weather in AK, so we often reserve a USFS cabin (12x12 with bunks, wood stove, outhouse, often a boat on the lake, etc). The State Parks and National WIldlife Refuge also have cabins to reserve - $25 to $45/night. Nicest ones we've used were in Haleakala NP on Maui ($75/night, but have wood stove with wood, cook stove with fuel, pots, utensils, and sleeping pads). Oh, wait, "huts" in New Zealand were even better - they offered laundry options. In Alaska, it really helps extend the season into 10-20F weather and is SO much better in the rain.
But, regardless: They're both avid readers so it is a given that 1-2 books (or ebooks) are along for each. We try to minimize electronics at home and during travel, but a rainy camping trip would be an exception and a fully charged iTouch is pretty light and lasts a while.
Card games, of course. Yahtzee is very compact (5 dice and copy the score sheets at 50-60% magnification). Play hangman for pretzels or M&Ms. Each kid has been thrilled to try his hand at carving a spoon or fork (with close supervision and safety lectures) there's an hour right there. One-match fire bulding contests.
Spreading a tarp 7-8' off the ground so people can have an outside place to stand up, stretch their legs and look around really helps the mental health. Pitch one up in the view direction.
Standing-room cabin tents are hardly SUL, but I've brought them on family trips (albeit more often on the canoeing than the BP trips) - not being bunched over all the time helps a lot whether that's a higher tent or a tarp outside the tent.