Hannover -Airport is nearest, then by train to Ilsenburg (around 2 hours). Another option is Berlin Airport, than by flixbus. That is cheap, but maybe the timetable does not fit (around 3 hours). Or from Berlin by Harz-Elbe-Express (cheapest train) to Ilsenburg (again timetable has to fit, around 3 hours).
Let us know when you arrive at Ilsenburg station and we will try to pick you up!