House Or Rental
We rented this Airbnb because it made more sense for us to have more space for visitors/getting ready. There are plenty of hotels and other house rentals around the area. So please book whatever makes the most sense for you! Please be aware that some hotel site include VAT (20% service tax) in their price and some don't when looking at rooms. Double check the price before you check out and don't forget to convert to USD (right now 1 pound = 1.35 USD).
Train
Edinburgh is not a car friendly city, so I advise NOT to rent a car, and instead use the public transportation. The Edinburgh Tram links all throughout Edinburgh, including the airport. The easiest way to buy a ticket, is to use your tap to pay credit card or apple wallet. Tap your credit card or phone at the gates and it will buy you a single adult fare. If you take the tram multiple times per day, it will cap your max fee at £5 (so you can ride all day for only £5!). Make sure your credit card has free foreign transaction fees! See link below for tram map.
Travel Note
Uber is also available for shorter/un-walkable trips if you prefer that over the tram