A lot of those things were on my list as well, so let me make a quick review.
Hakuhinkan was fine... a couple of floors with all kinds of toys, with some gimmick/robot stuff on the bottom floor. If you're doing Ginza anyway, it's a nice place to stay. If you do, you can go across the street outside it and find underground lunch places in a tunnel. That said, Sony building was completely lame. They didn't have anything really hot except for a few custom PS4 faceplates. Really. All the phones and cameras were things that were already out. So basically, you could take Ginza off your list if you're in a hurry. If you do go, you must check out the Lindt Chocolat Café. They make an AWESOME milkshake.
Go to Akihabara, to anywhere but Super Potato, and just browse for neat stuff. Akihabara is for selection, rather than price, but you might never find that cool thing again. Mandarake Galaxy and the Trader shop on the main street are well worth your time. If you want fighting or shooting games, look up HEY (Hirose Entertainment Yard), Taito's arcade. There is another Taito arcade which was dull - it has to be the real thing. If you want figures, check out Kotobukiya, or some of the shops right near the station.
Shinjuku Gyoen was very nice, we caught it right at the end of the sakura season. It's nice as a breather, especially if you're doing the rest of Shinjuku which can be... overwhelming. I wouldn't recommend Robot Restaurant, it looked obnoxious even from outside. The Capcom bar was rather nice if a little gimmicky. We didn't check out the Square bar. Try to have more courage than us and check out a proper hostess bar, and hope you don't get robbed/murdered by yakuza.
If you only have three days, I wouldn't recommend more than three areas. There's more than enough to spend a day at each. If you want to buy more cool stuff, you could split the Shinjuku day with going to Nakano Broadway. I'd also recommend Odaiba over Ginza, as it feels more modern and cool, rather than just expensive.
