Hi Peterli -
I agree that the "Dreiseenland" (country of the 3 lakes) is a nice place to visit. I'd include wandering through Schafis, Twann/Douane, and le Landeron. Public transport along the shore is merely OK. Certainly a walk from the church above Ligerz through the vineyards and down to Klein Twann or Twann, then along the main street is pleasant and easy, although quite hot in the Summer sun. The grapes like all that sun. Trains and lake boats, are available but basically transport is once per hour. Some other towns around the lakes are also charming. Le Landeron is a bit of a walk from the station. La Neuveville has some pleasant attributes, as well. I liked a short visit to Estavayer le Lac, on the other shore.
Murten/Morat deserves serious consideration. Although it is not a small village, and has a lot of tourists, it is still not very large, and it is nice to walk on the old town walls.it has nice atmosphere. Plenty of restaurants.
I'd add that a really pretty wine town - Motier - is across the lake (in this case, the lake is the Murtensee). Public transport to Motier is somewhat limited; some bus service and the lake boats. The vineyards rise on the hillside above the town, and the main street has the shops of the local wine merchants. Mr. Simonet makes some very good wines. I stay frequently in Sugiez, at the Hotel del'Ours. Sugiez itself has little to see. But, the hotel has wonderful hosts, a very good kitchen, and a cellar full of very good wines. Many local wines. There is a lake boat landing there, essentially at the hotel.
The whole area is a bit of a train ride from Lac LeMan (French name) or Lac Geneve, Swiss name. Probably, sine the Forum's official language is English, I should call it Lake Geneva. And, although public transport is certainly available, and enjoyable to ride through that part of the country, it is useful to have a car if you wish to see very many of the towns. Without a car, Murten/Morat and perhaps Motier become more appealing. Or, as you note, the western lake shore of the Bieler See near Ligerz. (Lake Biel.)
I'm away from my travel resources at this time, but wonder if something perhaps closer to their base, in the hills above the northeastern shores of the lake, might be worth considering. Villars... Nice train ride up the valley. Great views of the Dents du Midi.
Or, Mons Rotundus, which is the ancient Latin name for Romont, ;-). Quite a pretty village. .
Although I am perhaps incompletely informed, I find Geneva, even the nice old town around St. Peters, to be more like France than Switzerland....except for the plenitude of banks on almost every corner. ;-)