Neuchâtel has its own railway station with direct InterCity trains to Bern (25 minutes), Geneva (1 hour 20 minutes), Basel (1 hour 20 minutes), and Zurich (1 hour 45 minutes). It sits on the main line between Bern and Geneva, so connections are frequent throughout the day.
There is no airport in Neuchâtel; the nearest useful airports are Geneva (1 hour 20 minutes by train) and Zurich (under 2 hours by train). Bern airport is smaller but closer.
By car, Neuchâtel is about 35 minutes from Bern via the A5 motorway, 1 hour 20 minutes from Geneva on the same route, and 2 hours from Zurich.