You could try somewhere on Royal Deeside, Ballater or Bremar for example. From there you could easily visit a distillery as there are lots in the area. It's an easy drive from the airport to Royal Deeside. The Angus Glens aren't too far either and again an easy drive from the airport. Much will depend on what you like to do, outdoors and walks, eating out, Castles etc and also what time of year you are considering.
Aberdeen City isn't as nice as it once was. Lots of deserted shops, a LEZ and also "bus gates" seem to be putting off many folks from going into the City Centre. There is a bus service from the airport into the City and is probably the easiest way to get into Aberdeen if you don't have a vehicle. There is a train station at Dyce where you could get a train into Aberdeen or head North towards Inverness with many smaller towns inbetween to choose from.