I have a friend who has a Bed and Breakfast in Fleurier (Pain et Confiture) near me- and a couple of minutes from train station for commuting to Neuchatel. I am sure she would give you a special price for a longer stay out of the tourist season, if it can help. You can look at timetables on
www.cff.ch (click on English at top) - and I could help you scan local papers and agencies for adverts and with visits (if you pay my petrol).