gunmajet.net

The Do Nichi Kippu (Saturday/Sunday Ticket) offers unlimited JR rail travel on a given Saturday and Sunday in the Kanto/Koshinetsu and southern Tohoku . This includes all Shinkansen, express and local trains. It costs 18,000 yen, and must be purchased at least one day in advance (i.e. on Friday the day before travel).

Points of interest in this area include:

Matsushima - Scenic bay dotted by pine clad islets.
Tokyo - Japan's capital and largest city.
Yokohama - Japan's second largest city.
Kamakura - Small city full of temples and historic treasures.
Nikko - Site of Nikko Toshogu, Ieyasu's mausoleum.
Kawagoe - Former castle town known as the Little Edo.
Nagano - Former olympic city famous for Zenkoji Temple.
Matsumoto - City famous for its beautiful original castle.
Izu Peninsula - Peninsula with hot springs and beautiful scenery.

More information about the ticket can be found at the JR site:
http://www.jreast.co.jp/tickets/info.aspx?GoodsCd=666
or at Japan-Guide's article
http://www.japan-guide.com/e/e2357_002.html

This might not be the cheapest option for a weekend in just one of these locations, but getting the full value of the ticket in multiple stops wouldn't be difficult. So, if you're looking to knock out a bunch of tourist sites in one weekend, the Do Nichi Kippu is for you!