Imperial Palace Tour, Tokyo
The Imperial Palace is free to enter. You are given a ticket that looks kind of like a domino that grants you entry into the grounds. It's a vast area to explore. But one day here for a couple hours should suffice. Being that I was here in October, the weather was slightly chilly but manageable and cool. One of the wings near the museum was closed to the public, but the rest of the area, including the museum was open during the day we went. There is a lookout area where you can see the surrounding grounds. The museum has pictures dedicated to the Emperor's visit to 13 countries in the 1950's. There are relics from his travels as well.
The best thing about this place was admission was free. Which saves on the pocketbook and you get to experience a bit of culture as well.