I'll echo other's suggestion to spend a day in Kyoto and Nara. Kyoto in particular has a ridiculous amount of touristy things to do and see.
If you're into aquariums, the Osaka Aquarium is world class. They have a whale shark. It's exactly as cool as it sounds.
Food: Find a place that does Okonomiyaki. Eat Okonomiyaki. You're welcome.
You may encounter a man with a small food cart/truck at random, high traffic locations. It's almost always a good idea to buy whatever he's selling.
In general, any food place that looks humble will be both cheap and delicious.