We are avid hikers and will be spending a few days in Murren in July. Should we consider trying hut-to-hut hiking, or simply day hikes in that area?
First question: what do you mean by "avid"? Many of the hut routes are strenuous and a little dangerous.
Here's info on the one out of Murren:
On the other hand, if you are more interested in hiking among (rather than over) the scenery in the region, Murren has loads of hikes. They are all on this map:
If you are going to hike between Grutschalp and Murren, do it hiking towards Murren, so you are always looking at the mountains.
You could hike to Lobhornhutte (far right on the map), which is not that dangerous, but there is over a thousand ft. elevation gain.