The translation in LEO, visitor's tax, seems fine to me. There are also some past discussions in the archive.
In the US there's often a local hotel tax, but the hotels don't typically mention it, it just shows up as a line on the bill, since it doesn't usually have any special benefits like those you mention.
If the Kur is really a resort (with its own railroad? or is the Bahn like a tram or something else?), you might call it a resort tax -- or a resort fee, since a fee is often the word for what entitles you to benefits.
I suppose you could also call it a tourism tax if it's not either exactly a hotel or a resort, but somehow to me that sounds a little less welcoming to tourists, whom, after all, the town presumably wants to attract. I would be inclined to just call it a local hotel tax anyway and assume it's understood that guests in things like B&Bs also pay it.
And I would be inclined to play up the benefits in the explanation sentence, since the transportation pass sounds really nice. (-:
The hotel/visitor's tax that we collect on behalf of the city/town includes a guest card/pass that you will receive on arrival / at check-in. It entitles you to free/complimentary use of [local] buses and ?trams, as well as reduced admission to special events and leisure activities.
'Includes' probably isn't quite the right word in the original; I would assume that it helps support the city/town/resort area as well as covering the cost of the card, but anyway.