I am not sure if there is a campground right in the town, but there is Ferienplatz Brunnen am Forggensee which is on the Forggensee and has a bus stop closeby with buses that serve Fussen and the castles. I checked out my camping book and it states that you ride a bike or walk along the Forgensee right to the town. I stayed in this campground two years ago and it is a very nice place with excellent ammenities(ie shower/toilet building). There is also I nice little resteraunt a few buildings down from the campground which has great food.
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