Of course taking piano lessons (even self-taught!) is the very best activity to keep the mind sharp (Using these books!🙂 but since I already play, I study French daily, I read, exercise, cook and write. Anything that feels like a challenge for more than one of the 5 senses is the best though.
I do a few sudoku puzzles each day. I'm also brushing up on geography; starting with memorizing the state capitals. My geography knowledge has always been embarrassingly bad, and I figured it was time to remedy that. I've been a huge reader all my life, and try to read a bit before bed each night. Great to read different genres, I think that definitely keeps the old gray matter sharp.
I don't know if it keeps my brain sharp, but I have been crocheting hats for newborn babies and preemies for months now. I give them to 2 Hospitals in my area. You have to keep count of the stitches, sometimes I watch TV at the same time and mess up my stitches, so I really do have to keep count of my stitches. It keeps me busy and I love to crochet. I also do word search games.
I also crochet to keep busy, I also play brain games on my kindle and laptop or and sometimes my phone. Sometimes it is hard to crochet because I have a young cat, who thinks yarn is his. My current project with crocheting is making blankets to give to homeless shelters at the end of the year.