Jun 10, 2015 - 6:16 PM
I'm not sure if hut to hut hikes are what you're looking for. There are huts in high altitudes only, although the berghaus Arno mentioned offers a 'hut-like experience'. You could walk from Grindelwald to the berghaus (various routes, please see the map Arno linked to), and the next day down to Wengen or Lauterbrunnen (if you have strong knees).
There are wonderful hiking trails in lower altitudes too. Note that 20 km in a day is a lot in the mountains. Unless you only walk in the valleys, many routes include a lot of vertical meters. That's not a lot of fun for 20 kilometers if you're not into hiking.
Grindelwald to the Bachalpsee includes an altitude difference of more than 1200 m, for example. Once you have reached the lake you can proceed to Berghaus Mänddlenen or Hotel Faulhorn, provided that it's open. It opens mid-June as trails are snow covered before, and still might be until July. The next day you could reach Schynige Platte and take the cogwheel train down. This route might be too ambitious.
You may also want to consider the Jakobsweg, a trail along lakes and mostly in lower altitudes: www.jakobsweg.ch.