If you want to feel a bit of the thrill, head for Dawson City. At its height, Dawson City was called the Paris of the North, and it was the Yukon capital. There are a number of spots where you can pan for gold yourself, including Claim #6, a spot on historic Bonanza Creek, where all the excitement broke out in the first place. If you prefer more conventional gambling, try your luck at historic Diamond Tooth Gertie's Gambling Hall. After that, round out the gold rush experience by spending the night in a (former) brothel.
In the territorial capital of Whitehorse, you can tour a restored gold rush-era sternwheeler, the SS Klondike, or learn about the region's ice age history at the Beringia Centre.
If you're feeling more adventuresome, you can follow the Chilkoot Trail, in the footsteps of the many prospectors who left Skagway, Alaska, on a 53-kilometre trek now recognized by the U.S. and Canadian governments as part of Klondike Gold Rush International Historical Park. Back then, the isolated trail was tough going. It still challenges hikers today, but the spectacular scenery makes the trek worth the trouble.
Then again, spectacular scenery seems to be lurking behind every corner of Yukon (the locals usually drop the "the" and call it just "Yukon"). Kluane National Park, for example, offers you immense icefields, lush valleys and Canada's highest mountain. As the spot where the Pacific and Arctic air masses meet, Kluane offers an unusual diversity of animal and plant life. The area is particularly known for its abundance of Dall sheep.