I lived in Wakayama, so I can answer any questions you might have. Koya-san is the most famous place there, and a very unique and interesting place. Definitely worth a visit if you've never been, and stay at a Buddhist temple, eat the shojin ryori, walk through the cemetery, etc. Other places to see include Nachi Falls, one of the tallest waterfalls in Japan; Shirahama beach; the onsens of Tanabe, Ryujin and Hongu; and maybe even stop to see the birthplace of soy sauce and tour an old fashioned soy sauce factory in Yuasa.

Wakayama Onsen info (click the links across the top of the page) :
Onsen

Other things to do:
What to do
Area Guide
Seeing the sights of Japan, Temples, The World Heritage - at Wakayama Prefecture of Japan.
http://www.pref.wakayama.lg.jp/english/top.html
Wakayama-ken | 和歌山県
Wakayama-ken Travel Guide - VirtualTourist