For a hand-picked selection of brain teasers across easy, medium and fiendish levels, have a look at the adult puzzle range at https://phantom.everburninglight.org/archbbs/viewtopic.php?id=672153.
Think about space and time too. A large jigsaw needs a table or board where it can stay out for days, which is not always practical. Puzzles can be a calming, screen-free way to spend a wet afternoon, and working on one together is a quiet way for a family to sit down side by side without a fixed finish time.
Playing time is worth checking before you start. Many escape games run for around an hour to ninety minutes, so it helps to set aside a clear evening rather than squeezing one in. Some are single-use, where you mark or fold the components as you go, while others can be reset and passed on to friends once you have finished, which is handy if you want to share the fun.
The trick to a family game night that does not fall apart is picking games that work across ages. Younger children lose interest when a game runs too long, and older players switch off when the rules are too thin. A mix of one quick game, one party game and one slightly longer game usually keeps everyone at the table without anyone getting bored or overwhelmed.
Solo puzzle games are useful when you need to keep one child occupied without a second player. The Genius Square and Genius Star are self-contained, so a child can roll, place and solve on a tray table or a picnic blanket without anyone else joining in. Card games such as Flip 7, available from The Happy Puzzle Company, come into their own when the whole family wants a quick round at a campsite or in a holiday cottage.
The 3D and giant multi-storey versions bring something new to the classic. Instead of a flat board, counters travel up and around a tall structure, with the snakes and ladders running between levels, which children find far more exciting to watch. Larger garden versions scale the whole thing up for outdoor play, so the game moves from the kitchen table to the lawn on a sunny day.