Getting Around In Tokyo 1st Time?

Ok,so I'm planning on taking a trip to Tokyo, Jp (mostly visiting the Shibuya, Shinjuku and Harajuku areas.) with my friend.It'll be my first time there and I have some Questions and Concerns:

When I arrive in Jp, how would I be able to travel/locate my hotel/hostel etc. from the Airport?

If I plan on taking the subway/public trans...is it difficult to get around?

When do the trains/subways usually stop running? (Example, doesnt have to be specific.)

And finally, when I arrive in Jp, how will I be able to catch a taxi?

Being from Nyc, Im used to a certian amount of Hustle N' Bustle, but Japan, though an interesting place to visit it seems, is HIGHLY busy and not as easy to commute around, so it seems.

BTW, what do you reccomend me and my friend do while in Japan? (Any attractions or popular things to do?) We're young so we'd like to do things that are fun but responsible. Thanks. :)

how would I be able to travel/locate my hotel/hostel etc. from the Airport?

Depends on where it is located. Most likely by bus or train:
http://www.japan-guide.com/e/e2027.html

If I plan on taking the subway/public trans...is it difficult to get around?

Not really. Here are some basics:
http://www.japan-guide.com/e/e2016.html

When do the trains/subways usually stop running?

Around 1am.

And finally, when I arrive in Jp, how will I be able to catch a taxi?

By going to a taxi stand or waiving one down:
http://www.japan-guide.com/e/e2021.html

BTW, what do you reccomend me and my friend do while in Japan?

Some ideas:
http://www.japan-guide.com/e/e623a.html