When i visted mykonos in 2003 hard rock cafe had a restaurand outside the city center in the road to anomera (Car or vespa needed)
I have been 2005 and 2006 and this restaurant was closed. There is a place named FLIX on the sourroundings but i think is for 100% greek people (not sure).
The picture on Pakistaniguy tips seems to bve located on the city center, but i dont recognize the place.
The Hard Rock is a lot of fun, but be careful if you're island hopping on a cruise boat because you WILL lose track of time and you may miss the ferry to your ship!
The Hard Rock functions as touristy shop by day and a night club by night, if your still sober enough they even have a go-cart track that you can race on.
Dress Code Casual, it's an island atmosphere after all!