You can see one of the most beautiful night view of the Rainbow Bridge and the Tokyo Bay.
I recommend ending up the day with the night view of the Rainbow Bridge and the Tokyo Bay, the most beautiful night view in Tokyo I would like you to see.
Please choose the spots of your interest and let me know.
East Gardens of the Imperial Palace will take approximately one hour and a half or so.
Asakusa will take more than an hour if you would shop there, too. Tokyo Sky Tree will take more than an hour.
Meiju Jingu Shrine will take approximately one hour.
For shopping, Takeshita Street in Harajuku is mainly aimed for teenagers, Ginza has one of the biggest UNIQLO shop, Nissan Crossing and Ginza Six,which has an excellent Art book store, and Nihonbashi is the place for the mature that locals will also do shopping with high quality items, not the cheap tourist goods.
For typical tourist souvenirs, you can get them at places like Asakusa, Tokyo Tower, Solamachi: Skytree town and Akihabara.
About observatory, I will try to include some free ones near the spots we will visit.
Tokyo Sky Tree is 634m high, but a little bit distant from the Center of Tokyo and surrounded by lower buildings, so you might find Tokyo Tower (333m) or Tokyo City View in Roppongi more satisfactory to see the Contemporary Tokyo.
If you're interested in roses, I could take you a park (admission free) with beautiful ones.
If you prefer to see streets with good ol' days atmosphere of Japan, please tell me.
(If you're interested in cherry blossoms which blooms during winter, we can see them at the East Gardens of the Imperial Palace, Hibiya Street, huge Shinjuku Gyoen Gardens, and Ueno Park.)