By train, bus, plane

By train

SNCF, network map, Plan a trip, timetables at train stations and for print-out
For tickets from Germany: Deutsche Bahn and from anywhere in Europe: Trainline [FR], [DE], [EN]
Closest train station from house is Laveline-sur-Bruyères (8.7km, 10min drive)
- TER Lorraine, TER Lorraine map, train 13 from Strasbourg or Epinal (timetable or here)
Alternative train stop: Munster (Alsace)
- TER Alsace, line 19: Colmar-Munster (Metzeral) timetable, Selestat-Ste Marie aux Mines
More trains stop at:
- Saint-Dié des Vosges (32km, 41min), (directions)
- Epinal (35km, 43min), (directions)
- Remiremont (32km, 27min), (directions)
- Séléstat with continuation by bus: Selestat-Ste Marie aux Mines
- Colmar
Service for kids travelling alone with SNCF (€30 extra)
Bus connections from TGV train stations

By bus

Livo network: timetables of all buses, netwok map, plan a trip
Bus 28 Gérardmer-Bruyères (timetable, route map) stops in front of the church in Granges
Alternative (but not through Granges):
Bus 17 Gérardmer-St. Dié (timetable, route map)

By plane - nearest airports

Strasbourg Entzheim, France (SXB) (110km, 1h40) (directions)
EuroAirport, Basel-Mulhouse-Freiburg (MLH, BSL) (120km, 1h50) (directions)
Metz/Nancy Lorraine, France (ETZ) (150km, 2h00) (directions)
Karlsruhe/Baden-Baden Baden Airpark, Germany (FKB) (170km, 2h20) (directions)

A very good search site is ITA Matrix Airfare or Google flights. To search jointly for all above-mentioned airports use 'SXB, MLH, BSL, ETZ, FKB' for destination.