The sentence might look clearer if there is a comma between 'sophisticated ' and 'alfresco'; both of these words are adjectives which describe 'experience'. It's not a 'sophisticated alfresco' -- it's a sophisticated experience, which is also an alfresco experience. sophisticated - clever, interesting, alfresco - outdoors. Italian, but also used in English.

"Al fresco" in English means outdoor dining. Despite the Italian origin of the phrase, it is not used with the same meaning in Italy (as Ivan83 pointed out). We've re-adapted it with our own meaning. I've just found a few links where the expression is explained back to the Italians - seems they find our use of it rather odd. :)

'Sophisticated alfresco' normally means being outside in an elegant/sophisticated environment. Although in your example they are using sophisticated to refer to the type of food/menu on offer. Some restaurants offer sophisticated alfresco dining. In which case it means they have an outdoor terrace or garden where you can eat in elegant surroundings. As Neal said 'alfresco' is an Italian word which literally means 'in the cool air.'