5 day Japan itinerary

Hi,

A friend and I, both in our early 20s, will be arriving in Tokyo on July 27th at 16:00 and departing Tokyo on August 1st at 14:00. We know it's a short visit and impossible to get a real feel of Japan in that short amount of time; however, what are things that we absolutely must see? Is it worth making a trip outside of Tokyo given that we have such few days? If so, where to?
We are definitely interested in experiencing Japan's nightlife. We are also interested in seeing sumo wrestling and doing some shopping (not high-end).

The following I posted some time ago:
During one of my business travels to Japan I had a friend with me, first-time visitor and knowing he will not be able to return the next 15 years, he wanted to see ALL, but we only had four days for sightseeing. So we did:
day 1
Tokyo: Asakusa - Akihabara - ImperialPalace outer area - Marounuchi - Ginza - Daiba - Shinjuku with view from Met Office Bld, sushi at a conveyor-belt sushi restaurant.
day 2
Tokyo - Hakone ( the round trip ) - Odawara castle from outside ( just to see one castle ) shinkansen to Kyoto - jap dinner, bath and stay at ryokan near station
day 3
Kyoto ( city bus day ticket ): Nijo jo - Ryoan ji (garden) - Kinkaku ji - Daisen in (garden) - Ginkaku ji - Heian jingu (outside only) - Kiyomizu dera - Kyoto station Shinkansen to Tokyo, bento box dinner in the train.
day 4
by Shinkansen via Utsunomiya to Nikko till early afternoon ( temples only not the lake ) back to Tokyo-Ueno - by subway to Higashi Ginza for one act Kabuki play.
Please be aware; this is sightseeing pure.

If you will visit Japan again in the future, concentrate on the tourist attractions in Kanto(especially Tokyo and Nikko)this time, and land on Osaka and visit the western historical Japan next time.

This would be the best plan for the tourist with little time :)

As noted, you won't be able to do too much, but here is a simple guideline of what I THINK you can cover in 5 days

1/2day - Yokohama
1/2day - Harajuku
1 day - Shinjuku, Shibuya
2 days or 1 day - Daiba
1 day - Akiba, Ueno, Asakusa (Sensoji), Roppongi (Tokyo Tower)

IF you choose to do 1 day in the Daiba, then you can do full day in Yokohama, which also offer a few nice attraction and museums. There are several museums that you can visit while you are there

And if you want to try an Onsen, you can give it a shot at the Daiba

I guess it's a matter of preference -

- if you go for ONLY the "big city" experience, you could take it somewhat slow and stay in Tokyo/Yokohama area only, and do as "godwine" has suggested.
- if you also want a bit of traditional Japan - temples and nature as well - but not spend too much time on trains, then as "Ts" suggested, you can cover Tokyo, plus a side trip to Nikko for a day trip (or overnight if you want hot spring experience; not much nightlife up there).
- if you think this is the once-in-a-lifetime trip to Japan, then you can split your time between Tokyo and Kyoto. "Peter"'s itinerary looks quite intensive to me, that I would just do Tokyo and a round trip to Kyoto (meaning skipping Nikko or Hakone).

Read up on wherever you decide on going. That will make the trip worthwhile more than going to a bunch of places that you know nothing about.