Go for a run or walk around the palace. Coffee at a Cafe. Brunch at hotels. Watch the hungover crowd straggling home from Roppongi. Go to Yoyogi Park and watch the dog walkers. Wild Bird Park. Shinjuku Gyoen. Hama Rikyu and a boat ride up the Sumida River. Swimming at the Sendagaya public gym. Meiji Jingu Ice Skating.