There are three main airports you can fly into in Scotland - Edinburgh (EDI), Glasgow (GLA) and Aberdeen (ABZ). Aberdeen is 30 miles away from Drumtochty while Edinburgh and Glasgow are 100 and 130 miles respectively. All are straightforward to get to the castle by car or train. We would recommend making your choice based on your itinerary for the days surrounding the wedding (see things to do) and flight times.
Direct to any main airport in Scotland is obviously the most convenient but try to be as flexible as possible with stopovers when booking flights from the US. Consider booking the two legs separately and try multiple different airports for a stopover (e.g. London, Dublin, Manchester). All of those listed have direct flights to Aberdeen, and Manchester is a do-able train ride to Edinburgh (3.5 hours).