Edinburgh is about 20 minutes or 2 miles from Ocean Terminal where the ship docks
http://www.oceanterminal.com/
Go to this site and you can ask questions also
reply sent me was "cruise liner terminal is only a 5 minute walk from Ocean Terminal, in fact you'll be able to see the rear of the mall as you disembark from the ship and we are around 2 miles from the city centre. You can either use the local buses which you can catch from outside our main doors or use our taxi rank and it is also possible to hail the black cabs.The price should be around £5 from here to Princes Street but it does vary depending on the taxi company. "
Rob