Things to do in Mykonos?

Travelling to Mykonos soon and staying at Koukoumi (the vegan hotel). Would love to know about any day trips that were "vegan friendly" - i.e. winery tours, catamarans, day clubs, etc. that were accommodating if snacks/meals were included.

Also, if you stayed at Koukoumi, is it worth getting full board, half board, or breakfast only? Any input would be great.