I'll throw my hat in the ring on this (although this is largely focused on Tokyo). This is just excerpted from an e-mail I wrote to some friends:
I am not 100% confident on this, but if memory serves me correctly it is very expensive to take a taxi / towncar from NRT into the city (in the order of $200 and that was when the JPY was relatively weak against USD and it has since gotten stronger, so could be up to like $240 USD equivalent now).
There are other options, so don't be too alarmed. There are definitely coach buses that go to and from on a regular basis. I think they were reasonably priced ($30 ish per person?). There are also trains. Japan's rail system is very efficient, clean, and timely. I think the trains were about the same price as the buses. I imagine buses only have 1 or 2 drop off points. Traffic may be bad depending on what time you are arriving, so trains may have an advantage there for ferrying you into city quickly. The upside of the train system is that you ought to be able to switch around to different lines at a major station once you arrive in the city.
As far as what to do with your time once you arrive, I'd say you should definitely try to get a good meal in. There are amazing restaurants in Tokyo (for frame of ref, Tokyo has ~140k restaurants where NYC has 50k). Obviously there are amazing sushi places, but I'm not a huge sushi fan so pick that on your own if that appeals to you. I would recommend doing sushi, tempura, tonkatsu, ramen, or shabu shabu/sukiyaki. Japanese are really into specializing, so you might go to a place and it's solely a tempura restaurant, or they only have ramen, etc. I would personally recommend a restaurant called Maisen ( http://www.mai-sen.com/
) which is known for their tonkatsu (breaded pork cutlet). It is tucked away in the Omotesando area, but it is well known so if you have it written down you can ask. I would recommend locating it on a map 1st, though. It is a fairly big restaurant for Japan and does brisk business at lunch. Patronized primarily by Japanese, very authentic, and I believe for most dining rooms here you take off shoes and sit on the floor. Reasonably priced (maybe $20-25 ish for a set / prix fixe lunch). Walking distance from Harajuku and Harajuku station, but closer to Omotesando station (a couple blocks behind Omotesando Hills shopping mall).
Another good option for food (although likely more pricey) is shabu shabu or sukiyaki. This is a Japanese style meal where you cook thinly sliced beef in sauce at your table. It's kinda like a cross between Korean BBQ and teppanyaki. We have been to multiple shabu shabu places in Tokyo, but I don't remember what they were called. Just make sure it's not an all-you-can eat one. The prices vary accordingly with the quality of meat ordered (basic is like $30 per person, and Kobe beef is like $60 per person). You get a bunch of other things with your beef (soup, salad, veggies, maybe even sherbet at the end). I feel like we went here, but can't confirm (http://www.asakusaimahan.co.jp/english/index.html
). If you search around in a travel guide, I am sure they will recommend at least one sukiyaki/shabu shabu place. We might have been to this one as well (http://roppongi.shabuzen.jp/
) as that is in Roppongi.
To-do. I would recommend you take the train to Harajuku station and walk thru Harajuku down Takeshita Street which is an epicenter of teen culture. Lots of funky Japanese kids decked out in absurd apparel, weird stores, crepes, just a sight to behold. You can walk down to Omotesando area from here (which has a lot of fancy shopping such as Dior, RL, Paul Stuart, Louis Vuitton, etc.... although there are like 50 LVs in Tokyo I swear). Cutting thru Omotesando is a street called Cat Street. No idea what the Japanese name is for it, but it is commonly referred to as Cat St. Take this south towards Shibuya. Lots of really cool shops on Cat Street. Feel free to wonder off in the alleys etc as there will be stuff to see. Places off the top of my head to check out are any Ships stores (kinda like a Japanese J Crew), Journal Standard, United Arrows (different stores have different levels of clothing / different focus, prices anywhere from $50 to $5k depending on the particular store). As you head into Shibuya, if you see a store called Tomorrowland, it is very very cool. Not sure if it's men's only, but it's just a great store (think it's on Aoyama Dori which runs more or less parallel w/ Cat Street). As you go into Shibuya, make sure you go to Shibuya Crossing which is where there are like 12 different intersecting crosswalks and tons of people all the time. There are weird things here like arcades, and crappy teen clothing stores. Lots of neon lights, etc. The Tokyo you see on tv and in movies. Shibuya has a major train station and I would hop on a train to Shinjuku (4 ish stops maybe?). Shinjuku has a lot of department stores. I'd check out Isetan if you have time (they have a men's store which is incredible). Go to the basement of a high end dept store and they will have a big food court / grocery store with everything imaginable including disgusting Asian delicacies, $200 melons, wonderful French pastries, great gelato, etc. I would also recommend Beams which is a very cool store with men's, women's, and homewares (http://www.beams.co.jp/en/shop/east/shinjuku/beams-japan.html
). There are lots of different things in Shinkjuku, malls, restaurants, hotels, etc.
I think Tokyo is mostly about experiencing the street culture so it is a great city to walk around. I don't think the area near the Imperial Palace is all that exciting and the palace itself isn't much worth seeing. I'd say save that for some other trip.
The area called Roppongi is new and kind of hip, but it seems kind of manufactured. With limited time, I wouldn't spend much time (if any) over there. If you're there at night, however, there is a bar called the Cavern Club which has Beatles cover bands play (all people in the bands are Japanese) and it's really really awesome. Cover charge of maybe $25 but includes a drink I think.
Most of the better temples are outside the city, so allocate your time accordingly if this interests you.
Tsukiji fish market is only open during the early morning and kind of in a boring part of Tokyo, but it's interesting especially if you are jet lagged and up early.
Other things to note. People speak pretty bad English on the whole, so be prepared for that. There are many places (including restaurants and shops) where credit cards are not accepted. Japan is still very much a cash economy. So it is best to have some cash on you in case you run into a situation where you need it. Finally, tipping is not expected and is warranted only when someone truly goes way above and beyond the call of duty.
Hope this helps. Sorry it's a bit lengthy.