How do you have this problem of idleness innawoods? I go camping regularly, and even though it's only basic trips, there's hardly ever any time to sit around wondering what to do. We've brought stereos, radios, electronics that hold charge, books, cards, games, but none of it ever ends up being used. Between splitting firewood, lighting a fire, cooking, planning meals, prepping for hikes (in SHTF I guess they'd be scavenging or hunting forays), drying clothes, cleaning cookware, cleaning up inevitable mess and clutter in the tent, and a myriad of other chores I very rarely find myself idle. What free time pops up is spent on observing and discussing the local fauna/flora (in SHTF think scouting I guess), imaginary survival situations (what if we didn't have any matches?), stargazing (learning constellations is a useful survival skill) and just discussing the thoughts that pop up in the timeless peace and quiet of nature.
On solo trips I did occasionally find my mind wandering, but it's not unpleasant and constant physical activity is a sufficient distraction. I always thought that whittling wood to make various tools trinkets (cutlery, plates, spears) or writing a diary would be a nice downtime activity but never had much downtime.
With 2 or 3 people the sky is the limit if you're good friends. And if you're going innawoods together you should be good friends. If you're not, the obvious thing to do is to get to know each other, and get used to dealing with the parts that you hate. That alone will keep you occupied for a long time. I think people underestimate the sheer gravity of constant, forced social contact. It's like living with a bunch of siblings in shared bedrooms, in pre-internet times.
If your SHTF is expected to last say a year or more though, I think mental stability becomes a significant concern and books are necessary. Books with survival skills so that each page can expand into days of practicing the skill. Classics of philosophy, history, fiction, math which can likewise be pondered for much longer than it takes to read the book and also preserve important culture. College textbooks with plenty of exercises so you can learn useful chemistry, biology, engineering, etc. skills. I would put them all on an e-reader with solar charger, for portability for energy efficiency (kindle battery can go for month+). But to be honest, a lone wolf or small group in such a serious SHTF is pretty doomed anyways.