Yet another vote for Limousine Bus. I've been to Tokyo six times for TGS, and taken LB five of those six. The one year we took the train was hellish what with all the luggage transfer and dragging everything up out of the underground station. Just get on the bus and watch the countryside roll by. During rush hour it can take up to 2 hours, but after being on a plane for 13 hours it's like a vacation in and of itself.
I do recommend the train going back to the airport if you want to get there quickly, but Limo Bus is just as serviceable out as in.
As for food, listen to the people saying you can get good food for cheap by just going into any storefront you find. I love the places where you just pay into a vending machine, pick your meal, get a ticket, and then by the time you walk up to the counter with your ticket, your meal is ready.
And for the hell of it, I'm going to tell you how to get to the best ramen joint I have ever personally eaten at:
1. Take the JR to Shinjuku
2. Exit the station and head to the major intersection with the gigantic Starbucks.
3. Cross the street and follow it up past the left side of the Starbucks
4. Continue following this street. You'll pass a SEGA arcade at one point on the left. One of the cross streets will also have a Condommania store plainly visible on the right.
5. The street ends at a vague T-intersection. You'll see the Outback Steakhouse sign (tnw am cry) on the second floor of the building at the end of the street.
6. You're looking for Hachiban Ramen, which is on your right maybe 100 yards before the end of the street. It's marked with a big red paper lantern, and inside is a long bar counter and pictures of Godzilla movies on the walls.
7. Order their number one (i.e., most popular) dish (ichiban).
8. Enjoy the sensation of eating ramen so succulent and tasty it is like a pig crawled into your mouth and hugged your tongue.
It's about 900 yen, opens at 11AM. Unbelievably good.
Chuodori will take you across the river from Tokyo station as well.
