In 2013 I took a 3 month road trip and did Northern BC, Yukon and Alaska.
Places I recommend visiting and hiking:
Chilko Lake, camped there for two days and day hiked, there's a beautiful spot (to hike to) at the top of a mountain (Tullin I think) on the north part of the lake.
Bella Coola - Rainbow range and then hunlen falls - hunlen falls had a washed out bridge and didn't try it. The raindbow range had snow so I bailed and went to Haida Gwaii
Haida Gwaii, rennell sound, grey bay and tow hill - beautiful!
Hyder and Stewart BC, very beautiful, worth visiting no overnight hiking
Atlin Lake, if you are into canoeing/kayaking you could have a great time, I did a quick hike up Monarch mountain (I think is what it was called) and just hung out at the beach. Beautiful lake and views there.
Drove to skagway, tourist town but there is the famous chilkoot pass. I didn't do this hike because I couldn't be bothered with logistics.
Haines Junction was primarily a base camp to visit haines and hike the cottonwood trail and slim's river west to the top of observation mountain, YOU have to do this!
Then drove through Anchorage (spent only one night there) then on to homer just to check it out. Then drove to Seward for a cheesy boat tour for a day, the boat tour was expensive but worth it.
Denali State Park, Kesugi ridge, supposed to be great views of Denali but fog the day I visited (didn't do the whole trail).
Denali National Park, spent three days in a management unit, amazing!
Biggest regret of the trip was not going to the Gates of the Arctic National Park, don't make the same mistake.
Drove the top of the world highway to Dawson, most beautiful views (driving) during the trip. I think what made it stand out was so few cars on the highway.
Tombstone Territorial Park hiking 4 days on the trails there (up the Dempster highway). Beautiful park and trail.
I regret not trying to drive to Tuktoyaktuk, or driving through Nahanni or to Yellowknife
Then drove back down the Alaska highway to the Rockies, there I did the skyline trail, mount Robson trail (don't skip snowbird pass) and a hiked to Egypt lake. I'm missing a hike in there somewhere. Also visited Lake Louise, Canmore, Jasper and Banff.
There's tons of stuff to do on a trip like this, make sure you have 2-4 months to do it!
I had a 2002 Honda civic, it was fine on the Top of the world Highway but I wussed out on the Dempster, I'm sure it would have been fine though.