[komon]

I'll second speedsolving. I'm also big fan of fewest-move competitions. You get a scramble, an hour, and a sheet of paper. The current record in-tournament is 19 moves.

One thing parallel to speedsolving that is fascinating is the amount of optimization that goes into the cube itself, especially from small brands in China. Rubik's Cube engineering just happens to be in that sweet spot of providing incremental improvements, a large design space to eke out new and interesting optimizations, and cheap plastic manufacturing. The latest and greatest model that everybody is hyped about is just $15 + shipping from Hong Kong, so it doesn't break the bank.

YMMV, the only thing you might say negatively about it is that as a community, older players weed out very quickly. The demographic really leans in the 10-15 range, so you might struggle to find adults to talk to other than online.

It's also a practical application of all that group theory the internet's been telling you to learn.