I assume you mean the hilton in shinjuku?
I'd suggest catching the Nex back to the airport as it will give you more time and you know it will be on time, on a trip this quick an hour extra can make a difference
I enjoy the imperial palace but it's better in spring and I know a number of others who are a bit ho hum about it
If you like sushi it's more than worth the effort to do early morning as Tsukiji, as has been mentioned while the auctions may be finished very early the small sushi places are still open and there's still some dodge the out of control 44 gallon drum action for entertainment. From there I'll wander up into ginza stopping at the nissan gallery for a coffee (which has a brand spanking new GTR sitting in there atm which excites me but will probably leave most people scratching their head saying "a what?"). From there you can keep heading up ginza to look at the shops, sony centre etc and would leave you enough time to continue on and get to the imperial palace
Make the effort to head out into shinjuku the night you arrive, grab some noodles from the wagons and play some pachinko
If you're into cameras the camera district just west of shinjuku station is worth a wander but if you're buying the camera alley at nakano is easily the best prices (with amazingly cheap top quality second hand gear)
The odaiba area has a lot to see, amazing architecture, maritime museum, Toyota megaweb/museum, kind of a taste of the new
Asakusa and the river ride is a great suggestion, especially if you're not in the mood for lots of walking
