Castles near Tokyo

I'll be visiting Tokyo for a week and would like to see a castle. I've seen Himeji and Ueno castles and am looking for something similar. Can anyone recommend some that are nearby Tokyo (Shiodome area is where I'll be staying) and are worth adventuring out to see? Thank you.

The closest castle with standing keep is Odawara, but it is a concrete reconstruction. If it is not too far for your preferences, I recommend Matsumoto Castle:
http://www.japan-guide.com/e/e6051.html

Other castles:
http://www.japan-guide.com/e/e2296.html

Matusmoto castle is one of the four National Treasure castles (along with Himeji), and one of 12 surviving orignals.

It will take about 3 hours to get there, and cost about 14,000yen round trip. You would need to travel to Shinjuku then take the Azusa express.

You could also go to Kakagawa castle. It was recently rebuilt in original materials and techniques, and there is the still inact original daimyo's mansion.

It would cost around 15,000yen on the Shinkansen round trip, and take about 1hour 45 min to get there.

Here are soem details of Kakegawa castle:

http://www.jcastle.info/castle/profile/48

Uji and Sandy, thank you very much for this useful information! I will be buying a rail pass (national or east, haven't decided yet) and will see if it covers travel to either one. They both, Matsumoto and Kakegawa, look wonderful and I wish I could visit them both...no time!