Lonely Planet has by far the most helpful guidebooks in English. Their Tokyo City Guide recommends hopping on the Yamanote train to get an overview of the city. The train goes around central Tokyo in a little more than an hour; when combined with an all-day rail/subway pass (¥1580), it gives you a good overview of the place. Here's the inside (counterclockwise) train pulling into Tokyo Station:
From Shinjuku, I went around to Tokyo Station, and walked over to the Imperial Palace. You can't get near the place, really; there's even a moat around it, in case of siege engines. I did wander the outer garden, dodging bicycles and Japanese tourists, and finding an unusual (for me) number of people doing watercolors:
Back to Tokyo Station for lunch in one of the crowded food courts, where I sampled three different kiosks and only bit into one thing I didn't like. (I must remember to ascertain what part of the chicken is on the teppanyaki stick.)
I decided not to try these, however; $15.50 was just too expensive:
After lunch I continued on the Yamanote train to Shibuya, which everyone who's ever seen a photo of Tokyo has seen. I plan to head back there around sunset to (a) get photos of it at night and (b) eat dinner in one of its thousands of little restaurants. Stand-up sushi, maybe? Itadakimasu!