Your interenary for Tokyo is pretty decent, heck I walked to Akiba from Shinjuku and you go through Shibuya getting there, killing two birds with one stone, took me roughly 2 hours to walk all the way. Took the subway back.
However Shibuya does have some killer buildings if your into architecture. Fashion row along with Catwalk St, that's a couple hours right there.
As for the Imperial Gardens, I found Shinjuku Goyen (which is actually the Imperial gardens as well) more interesting, it costs you I think 2-300 yen or so.
Awesome park !
You could throw in Meiji-Jingu as well, pretty cool Shinto shrine and a HUGE one at that. Pretty much next door to Shinjuku.
As for Shinjuku station heh ... it's got over 150 exits, one of the more popular places to meet up was/still is the Studio Alta LCD display. It's a seriously kick butt subway station.
Roppongi is worth a walk around during the day, some neat stuff to be seen
AVOID it at night.