One of the most popular places around here to ride bicycles is the Blue Ridge Parkway.
It's also, IMHO, one of the worst.
No bike lanes, no shoulders, stupid riders. By Federal law they must ride single file but they almost never do. At least on a motorcycle you can pass them. Sometimes they'll have 20 cars backed up as they go up a mountain at 1 mph.
I ride bicycles, too. Mountain bikes. Why anyone would want to mix bicycles and cars (unless you're commuting) is beyond me.
