There is a parking garage right by the Murinsel.

a great place to enjoy a nice wine in a nice ambience

This is a normal cafe and there is no entry. What is there is an arrogant service. The marble island can be visited for free.

The Mur island in and of itself is an attraction worth a visit. Especially the café from the inside, where the Mur rushes past the coffee table. Worth seeing. Must have tried.