Even if you don't end up buying/renting anything, I'd like to offer the suggestion that visiting musical instrument shops (and neighborhoods where there may be multiple music shops) can make for a wonderful, completely authentic backdoor experience.
I once shopped for (and ended up buying) an expensive musical instrument in Japan. There's a neighborhood in Tokyo where the streets are lined with specialty shops selling everything one could imagine (and more) in the realm of musical products. I spent hours in complete amazement wandering those streets and poking around shops, eventually I found the shop I had specifically been looking for, stayed in that shop for a couple more hours trying out instruments, eventually buying one. Nobody in the shop spoke any English (I speak no Japanese), which made it all even more of an adventure. It was so much fun, and I came home with a wonderful instrument (a high quality model, made in Japan for the Japanese market) that would have cost thousands of dollars more at home.
Finding specialty shops -- or even better, a neighborhood where there is a concentration of many specialty shops -- is a treasure for travelers. Always a delightful treat and worth seeking out. (This reminds me, I need to post a request for something like this in a separate forum.)
Electronic keyboards for keeping up with the piano lessons should be very easy to find. Very cool thing to do on your trip!