From 1 pm to 3 pm is two hours, not three, so you really donft have much time (?).
Here is what I would do, although obviously my tastes are probably different from yours. Weather depending, I would walk to Ginza, maybe stopping at one or more stores there, and then go to the rooftop garden at Ginza Six. Of course it isnft the Imperial Palace East Garden, but to be honest I wasnft particularly impressed with the Imperial Palace East Garden (or Hibiya Park, for that matter); they are okay but to be honest I enjoy the atmosphere and views from the Ginza Six rooftop more, and you will find a variety of greenery and flowering plants there (including, to my surprise, an gOctoberh cherry tree that still had some flowers on it in late November). If you are hungry, you can pick up some food in the Mitsukoshi or Ginza Six basement and eat it up there (one of the few places you can sit and eat purchased foods). On the way back, time permitting I might stop at the Starbucks Reserve cafe on Marronnier-dori street. (I am not really a Starbucks person but I find this place to be reasonably pleasant, and they have some interesting drinks and quite good pastries, not the usual Starbucks fare. It is a bit expensive, though.) Or maybe stop at the Itoya stationery store on Ginza-dori, or the Muji flagship store on Namiki-dori. The walk from Tokyo Station to Ginza Six is less than 20 minutes at a steady pace, and if you use Google Maps or something, you wonft get lost. There are lots of restaurants in Ginza and Yurakocho where you can have a late lunch if that suits you, and many of them are inexpensive.
Anyway, I really like just strolling around Ginza, and there are some nice stores there (not just luxury goods stores). Tsukiji Market is a little farther, but also within walking distance, and the gouterh market (with a lot of shops) is still active (the fish market itself moved several years ago). But I would consider Tsukiji to be essentially a tourist trap, and it gets terribly crowded. I would rather take a walk along the Sumida River, although in that area it isnft especially photogenic. (I just like walking along the Sumida River.)
Anyway, that is what I might do myself, especially if I didnft want to deal with taking a train or subway. If you donft mind that, the Tokyo Government Metropolitan Government Building (gTochoh) is actually not a bad choice, if it is a clear day with good visibility. People turn up their noses at it these days because there are flashier observatories, but those are expensive and crowded. I was at Tocho recently and it was very pleasant—no waits for elevators up or down, no crowds, and the views (including Mt. Fuji) were plenty good enough for me. And itfs free. But you do have to take transit to get there.
Ucofs suggestion to just stay around Tokyo Station is also good. (Ucofs suggestions are always good!) There are quite a few stores there, some of them inside the JR wicket and some outside. (So if you want to look at the shops inside the wicket, be sure to do that before you exit or after you enter, depending on where you are coming from or going to.) There are a couple of waiting rooms inside the wicket where you can sit and consume purchased food and beverages.
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