It is important for you to understand what region codes in relation to DVDs.
Commercial DVD manufacturers set region codes on the discs they sell. The United States, for example, is Region 1. Japan is Region 2. DVDs that do not have a region set on them are either called All Regions, or Region 0. Likewise, DVD players are supposed to have their regions set. Sometimes they are shipped as Region 0 and then get set the first time you play them. It is possible to purchase an all-region DVD player, but the normal ones you find in your local store will normally be for your region.
DVD drives on computers will allow you to change regions 5 times and then they will stay set to that region. It is possible to get software that overrides or fools the hardware into thinking you are still using that region.
I have linked to the Wikipedia article on region codes, where you can find out more details on how to defeat or live with these restrictions.
BLU-RAY - Japan and the U.S. share the same region code on BLU-RAY discs, so this might be a good alternative for you.
Academic libraries rarely have DVDs that are not purely educational or documentary. They will not compete with the rental shops in their areas. Public libraries will occasionally have them for the hearing impaired. Classical music CDs are generally held by academic libraries. Public libraries will also have more traditional music.
There are many rental shops in Japan. One of the most famous ones is called Tsutaya. There are usually 2 sections in Tsutaya: for sale and for rent.
There are also lots of used shops, where you can find DVDs and CDs that had been rented previously.
One of the questions I get is about buying Japanese songs/videos through iTunes. If you want to buy songs through iTunes you either need to have a Japanese credit card OR an iTunes Japan card. You can easily buy them while you are in Japan and use them after you return home.
Once you are back though, you can use an intermediary to purchase the iTunes from the United States. There is a markup to the cost, but it is better than not having access at all if you can't ask friends for help. JBOX.com has the instructions here.
UPDATE (2012) iTunes is now checking IP addresses, so even though you have a gift card and Japanese account, unless you block your IP address you can't use them.