I highly recommend the Appartements Alpha Graz and would certainly stay here again. The owners are very friendly, welcoming, and informative, the apartments are super-clean and quite roomy with all the appliances and comforts necessary for a short or longer stay. There is plenty of room for parking in the courtyard and, if you are without a car, the number 5 tram and taxis are practically at your doorstep. (Getting to the airport could from here not be easier.) The immediate location is not so interesting, but has a number of bakeries and supermarkets nearby for daily needs and you can get to the heart of beautiful Graz in 5 to 10 minutes, or a more leisurely 25 minutes if on foot.