The apartment is very nice and has everything you need. It is located in Castelmola which is higher up the mountain than Taormina. It is certainly easiest to have a car but there are also public transport possibilities and a stairway you can walk down to the city of Taormina. The bus takes 20 min to reach Taormina and by foot a small hour. The city of Castelmola is very small and charming and is a nice contrast to Taormina which is very full of turists. All in all, a very beautiful place, if you want to explore a lot in the area, I would recommend you go by car.