You can camp at the South Meadow trailhead for free, as well as park your car there...for free. You can take the South Meadow trail for 2.8 miles to Marcy Dam. It totals 8 miles to the Marcy summit.
I've climbed Marcy and neihbors many times. I grew up in the area and would seek refuge in the ADK's. Marcy is a great hike (as long as the black flies aren't out). The summit keepers ahve done a GREAT job at getting the summits on all the peaks above alpine in great condition...Keep ujp the good work. It is unfortunately being overrun by people. Another joy of the Adirondacks is canoeing fcrom the lower peaks up to the upper peaks. I've done that 4 times in my teenage years and haven't been back since. Its a great 4-7 day canoe trip that starts at longs lake and continues way up north. I really have to get back there some day. I live in Colorado now and am tackling some of these peaks and epipc hikes.
See you on the mountain some day.
As a correction in the distances from Marcy, as the crow flies, Camels Hump is ~86 km, Mont Royal is ~158, and Mount Washington is ~210. Not sure how to get the actual article corrected. Mt Royal is at an ~9 degree heading, Camels Hump at ~degrees, and Washington at ~84 degrees.