Is there bus or train transportation from Edinburgh Airport to downtown?
Yes there are bus links and also a tram. The best option depends on which part of town you need to get to. Here is a link to the airport website with transport details. Transport links from airport
If your hotel is within walking distance of the tram line that would be an excellent choice. Clean, quick, easy to use, and you can get a round trip pass if you desire.
Thanks Skyegirl and TC, good info.