This hike is a great one for a visitor to do rather than Flattop. For one, you get the drive to Girdwood. Second, you get great views, a good hike with varying levels of steepness, and a interesting juxtaposition of ski-lift technology, history, and rugged outdoors. Third, you get to mingle with fine diners and tourists on the tram chalet's deck (ok-- not always a bonus). Fourth- you have a bathroom and a tram down! Great for guests to see it all! Oh yeah-- you have Chair 5 to get a burger, beer, and/or pizza on the bottom. Anyway, I started doing this hike with friends who liked a challenge of racing to the top along the straight up path. It kills. But it is a good training route for other steep climbs. You start at the end of the old condos to the right of the Stizmark. You can park there for free, like most areas in Girdwood that I know of.
I have since started going up the Chalet's service road. Follow local's directions or the book 50 Hikes. It is hard to describe how to find it, because there are a lot of paths on the mountain. Anyways, it is not a "road" in the regular sense. There is NO traffic, and it has extremely steep parts for a road, loose rocks, bear signs, etc. In early summer it has rushing streams going through culverts. You go past seemingly abandoned ski lift stuff that is just waiting for the next winter.
Eventually you get to the Chalet and the old Roundhouse. From there you can go on (see the book, as I have not done so). I have always enjoyed the view and avoided the crowds if possible by scouting around. If you ski or snowboard it is strange to see the dirt. If you are a talker you will always find a conversation from the tourists AMAZED that you climbed all the way up that big hill. Get on the tram and it takes you to the Prince Hotel. From there ask for directions if you are unsure and do not want to take the paved road back. Head up the trail above Chair 7, then down past Chair 3 right above the Sitzmark/ old hotel-- you will see your car as you get to the bottom.
Sorry the description is so long-- there are a lot of hikes on the clear ski paths and access roads for sno-cats. The access road to the top is pretty different in that it is mostly rock and rough gravel. I heard it ices over in October and they close it. They do not allow hiking before sometime in June, I think. There may a fee for the tram down. Bears have been encountered on the access road, and in some ways it is more isolated than other paths, depending on the time and the weather and how many exercise hikers are out.
The Alyeska Resort is a great place to hang out and have a drink after the hike. The bakery down the hill is a worthwhile stop as well.