Help with a travel itinerary

For all you experienced Japan travelers, can you please help me with a travel itinerary?

I am being sent to work in Tokyo for 4 weeks, after which I will take 2 weeks to travel by myself. I have the option of renting the apt my company is giving me in Tokyo for $165/night or finding something myself.

Q1) Is this expensive?
Q2) Is it easy to take day trips to other places (i.e. Kyoto)? Should I stay in this apt and do several day trips from Tokyo or should I try to find places on my own?

I have 3 weekends in Tokyo, and then 2 weeks to travel, although not sure where to go and for how long, and not sure how to find hotels. I believe I have to return back to Tokyo for the flight home.

Q3) Any good ideas what I should do on the weekends in Tokyo?
Q4) Here's the fun part...where should I go in the last 2 weeks? I'm more of a nature/garden/temple/see traditional culture person as opposed to a museum person, but I'm open to anything.
Q5) How do you find places to stay while traveling?
Q6) Should I/how do I obtain a rail pass?

Ok, I know, a lot of questions, but I would really appreciate any help from the travel buffs out there! Thank you!

Q1) Is this expensive?

Depends on the apartment! For $165 per night you can stay at a high end 3-star hotel or a 4-star hotel if you find a good deal.

Is it easy to take day trips to other places (i.e. Kyoto)?

There are various destinations that are easily accessible from Tokyo, such as Nikko, Kamakura and Hakone. Kyoto is about 3 hours one way from Tokyo, and also possible as a day trip.

Any good ideas what I should do on the weekends in Tokyo?

Depends on your interests. A list of tourist sites:
http://www.japan-guide.com/e/e2164.html

Here's the fun part...where should I go in the last 2 weeks? I'm more of a nature/garden/temple/see traditional culture person as opposed to a museum person, but I'm open to anything.

Some ideas:
http://www.japan-guide.com/e/e623.html

How do you find places to stay while traveling?

I use the internet to reserach and reserve hotels. This website has links to many of them.

Should I/how do I obtain a rail pass?

About rail passes:
http://www.japan-guide.com/e/e2357.html

It sounds like you have the opportunity for an interesting visit to Japan, and there are endless possibilities for the travel portion. Staying in Tokyo and taking day trips is a not a bad idea but there are many places that are just too far for a comfortable day trip. I'd be inclined to head for the Kansai area for at least a week, and then pick one or more other spots for shorter stays to experience other aspects of Japan.

Depending on your itinerary, one or more rail passes could save you a whole lot of money. However, most of the better rail passes are only available if you enter the country with the status of Temporary Visitor. If you are engaged in paid work activities, even for a short term, you might not have this status. (See sections A and B under http://www.mofa.go.jp/j_info/visit/visa/03.html#a)

This is something to think about ahead of time. If you have the option, do not go on a work visa.

Hi Joe,
When I traveled around Japan, I had a volunteer guide from this group:
http://www.tokyofreeguide.com/index.php?ml_lang=en

I spent two days with them in Tokyo and the guide helped me with booking everything for my Kyoto and Hiroshima trip.

Thank you to all who answered me. If you want, shoot me an email at liquidinnovation@yahoo.com to keep in touch!