(Sorry, this is going to be long and my train of thought has tracks everywhere.)
We went to Tokyo for the first time last summer. I really have fallen in love with the city, so we're going back in two months to see the cherry blossoms.
We haven't explored outside Tokyo yet, as we weren't there too long. The next trip will also just be in Tokyo, as we have friends going who want to keep things as cheap as possible. Gives us an excuse for another trip.
The first thing I would suggest you do after clearing customs is to head down to the train area and purchase a Suica card. I think it runs about $30 to $35 and includes a one-way ticket into Tokyo on the N'EX and something like 1000 yen is put on the card. You can use this card for getting around town (subway, trains, buses and some taxi companies) and making purchases in subway stores. You can keep the card for future visits or request a refund of the balance.
There's also a free map book in the area where the Suica cards are sold that was perfect. It's a shame I lost mine in Odaiba on our last day.
Odaiba seemed lame to us. There was a Toyota showroom, Fuji TV and two malls that I remember. The water taxi from there was nice, as it was stinking hot in July.
Shibuya has a lot to see. Harajuku (Take****a Dori) and Omotesando Hills (another mall) are fun to browse through.
Metro - Hard at first. We were looking for the Marunouchi line (red circle) and were dutifully following the red circle symbols until they just stopped. From that point, instead of the symbol, they were using the word "Marunouchi" so once we realized that, we were good to go.
Toilets - As a female, I can recommend using the toilets in the malls, as they were nicer than the one we had at the Tokyo Hilton. By nicer I mean they had more buttons.
Metro toilets (for females) were either the trough or a standard public toilet that we're used to (no bells, whistles or perfume).
Below are parts of what I sent to our friends who will be coming with us in April:
Tokyo Food Show is located under Shibuya station. Anything you would ever want to eat (or possibly not) is located there. Downside is that there's no seating, eating on the street is frowned upon, so it's 'eat at home' food.
I hate to admit it, but we spent some time in various Starbucks around Tokyo as a rest stop. There's one at Shibuya crossing that's particularly good for people-watching. Fantastic people-watching, actually, since it's right above the pedestrian scramble.
The trains can get pretty crowded. I had one lady sitting on my left who (I think) kept talking to me in Japanese. She might have been arguing with the guy on her left, but I just ignored it. Perverts happen on the trains, but as gaijin, I doubt we have to worry.
Taxis start at around $7 and go up. Language can be an issue, but if you have an address or a map, they can get you to the area. Japanese addresses work differently. It's something like the neighborhood, the block, then a building number. There aren't street numbers, and the buildings are numbered in the order they were built. x| The cab doors open and close automatically and there's lace on the seats. Just fyi.
We didn't do Tokyo Tower last time because we were dog tired and it was about $18. We also didn't go up to the Tokyo Metropolitan Government Building's free public viewing floor, even though we stayed a stone's throw away. We might be able to see Fuji-san from there, since access is only available to him July-Aug.
Asakasa was interesting and photogenic, so I'd like to go back. Odaiba was overrated and deserted, although the Rainbow Bridge and water taxi were nice. Shibuya, Ginza and Akiba are definite, have-to, must-sees. I'm sure the Imperial Palace's East Gardens will be gorgeous and good for a few pictures.
Our sushi dinner (and we ate quite a bit if I remember correctly) came to about $40 total (two people, salad, lots of sushi, beers...sushi). There was a language barrier, but we got through alright with smiles and charades.
There are plently of cheap food options, though. There were some American crap chains (McDonald's, Wendy's, TGIFriday's), but there are also Japanese ones (Mosburger, Yoshinoya). 7-11's over there are nuts. They sell sushi, but it's not like the rotating hot dogs of questionable age that we deal with over here. Add 7-11 to the must-see list.