Not all that hard to reach from Basel is the Three Lakes Region.
The My Swiss Alps page doesn't have much on the Three Lakes Region.
I don't find the web site for the region to be particularly compelling:
Here are some links to discussions in My Swiss Alps.
[Please note that early in my post is a reference to the Emmental with a lot of pictures:
That region offers much of what you seek and is not far from Basel. There is train service to the larger towns, and buses to smaller ones. The Emmental is a hikers region, but many of the villages can be seen in easy walks from the bus or train stops. They are not very large. I'd spend some time with a map with aerial views, and think that Signau might have a pleasant main street for a walk. Trub, accessible by bus from Trubschachen or Langnau i. E., also deserves a walk..]
That link has several pictures from Ligerz.
Town names to look for are Le Landeron, Twann/Douane, Schafis/Chavannes, Ligerz/Gleresse, Moutier ( a wine village on Lac Morat/ Murtensee, and Murten/Morat(mentioned previously).
German and French names for almost all of the towns in the region because you are on the language boundary.
My photos are on my other computer, where I have some more general information on the region. I'll try to post that material in the next few days.
What I propose is a visit to Ligerz and Schfis, a ride in the funicular to the first stop ( Pilgerweg...Pilgrims Trail) a walk to the church and beyond, as far as Jlein Twann and Twann, then a lake boat to Murten/Morat.
For a really deluxe meal, get off the boat at Sugiez. Hotel de l'Ours is right at the landing. Book ahead. The terrace under the chestnut trees is nice in the summer, and expands the restaurants seating capacity.
From Murten, take the trains back to Basel.
The old town in Biel/Bienne is small but nice. 10-15 minutes walk from the station.