I am an American living in Neuchatel. It is best to just by a 1 way or round trip train ticket from Geneva to Neuchatel. There isn't a discount to buy round trip vs. one way. There are quite a few direct trains to Neuchatel from the Geneva Airport that make several stops along the way. The station is at the airport and It is a very easy ride from Geneva, about 1 hour. Train travel is not cheap in Switzerland but very clean, safe, easy and most of all very reliable. Let me know if you have any other questions.
Once you are in Neuchâtel, you should be aware that the local public transport network operates a zone system. The town centre and close surroundings are all in zones 10 and 11.
Within a given zone, tickets are valid on any route and any means of transport (bus, tram, train and boat). You can get a normal single ticket which is valid for two hours, or a 24-hour ticket valid throughout the chosen zone(s) for 24 hours - this is worth buying as soon as you go beyond one journey in a given 24-hour period.
You cannot buy tickets on the buses/trams/trains, you have to use the machines at the bus stops/stations before you get on. These machines take cash and cards.Edited: 01 April 2012, 22:48
Thank you very much for your help.