Ballon D'Alsace from the North side is 9.1 km at 6.8% average. Must just scrape into Cat 1 ...
I live in Brussels, and a friend dragged me along to follow a few stages. Threw the bike in the car "just in case", but the bike proved a godsend as it can be the only way to get into the roads/starts/finishes unless you like long walks.
Actually mowing the lawn and following the tour on the net or TV isn't a bad idea, you get a lot more info. It's very hard to get close to the riders at the start/finish, and then on the road they go past in a flash. Spent a very pleasant morning on Friday sitting in a cafe terrace in Germany with coffees and cake as the whole spectacle raced past, but the other days it was pretty miserable with the rain and all.
I'd definitely do the mountain stage thing again, though it's a whole day .. and then some. It took me longer to get down and off the top than it did to ride up. At the beginning of the day, to even get onto the climb I had to park the car about 10 km away (which was where the traffic slowed to a halt).
But .. a big buzz.