Kanika parking lot, you will see Anaplasys Gym, right across the street, on the street corner there's a gift shop. There you can find a full map of Limassol, map that also has a street index.
Not much to the tourist area to be honest, it only goes back a couple of streets. For general Limassol town try http://tinyurl.com/26h9a7 Tourist area, but only showing major hotels etc try http://tinyurl.com/24ab3l