Dawson City is amazing in the summer, and I would highly recommend driving up from Whitehorse. You will see beautiful views along the 5-hour drive and will head north where the sun is out all night long.
If you have time, I would recommend crossing the river on the ferry and driving up the Top of the World Highway (if you plan on driving the whole thing, make sure you have a passport as it does go into Alaska).
On your way back to Whitehorse, make sure you turn off down the Dempster Highway and drive to Tombstone Territorial Park!
Dawson is located in a protected area, so in the summer it is often HOT with very little wind, which makes it such a nice escape for Whitehorsians like me who may want to get away from the ever-present wind. Prepare for it to be nice and warm if you're visiting in the summer!
The entirety of Dawson City is a historic site, so the buildings are all either original historic buildings from the Gold Rush era or designed to fit the "historic" theme of the town, making the city feel like you've stepped back in time!
If you have a chance, I highly recommend doing a free Parks Canada walking tour. The guides are super knowledgeable (and dressed up in old-fashioned outfits), and you get to see inside buildings you otherwise wouldn't have access to! You can head to the Visitor Information Centre to book!