Book train ticket direct to La Chaux-de-Fonds. At Neuchâtel (from Geneva or south) or Biel/Bienne (from Basel, Bern or Zurich) change to local train. Be careful usually the changeover time is tight, only 1-4 minutes. We pick you up at the station.
There is a small airport for private airplanes at La Chaux-de-Fonds. The International airports suitable to access are Zurich, Geneva and Basel. All these have direct access to train except Basel where a shuttle bus takes you to the Basel train station. Train is the best way to travel in Switzerland.