A lot has been well said, certainly check out Alpine Roads, decide roughly where you want to go and then ask these guys about campsites.
Not much good asking too much about the "best" place in the Alps, it is 85,000 square miles (about same size as UK) and all of it good.
Get the "Motorcycle Journeys Through the Alps and Beyond Book" and choose a couple of places, this is what I did this year / doing again next year.
6 Days is quite short, especially if it includes travel and leaves you just four days, for that I would suggest just one or two locations.
For a few days Andermatt would be great, but it is high up and possibly a bit cold for camping, look for campsites below 1,000mtrs would be my recomendation or pay up for Hotels for the odd night, you will see Zimmer Frei signs everywhere in summertime and lots of Ski Lodges trying to get an extra few quid, so if your not pre-booking will probably find some great deals.
This is a great half way through france Stop-off, and worth a day or two if you had time:
http://twowheelmoorings.co.uk/default.aspx
Here are the regions as listed in my book, Red X's are on my must visit list, Andermatt is number one in the book, but the area only has 1-2 days riding, but you can do 5 tremendous passes in one easy day trip!
A-F are the easiest to reach so maybe look around there if you only have a week, choose a couple of locations with 2-3 nights at each.
Alternatively consider the Black Forest, not as spectacular, but the region can be covered in a week from a single base and it is only about 6-7 hours from Calais, and reachable in a (long) day from most parts of the UK.
I have posted details on this years trip here:
http://www.ukgser.com/forums/showthread.php?p=2513786#post2513786