la,
The Lauterbrunnen / Mürren area is indeed gorgeous and a wonderful place for hiking. The snow should be gone by mid-June, but of course no guarantees. One concern is that the local farmers spread "liquid fertilizer" in the spring, but I'm not sure when that will happen.
One nice hike from Mürren is to take the Allmend-Hubel Funicular up to the top, and then walk back to town. It's not so much of a "hike" as a "stroll", as it's all downhill. There's at least one hotel / bar on the way, so you can stop for a cool one if necessary. There are many other hikes possible in that area, and I'm sure the others in the group will be able to offer more detailed suggestions.
Switzerland is expensive, so be sure to budget accordingly. You might want to buy a copy of the Switzerland guidebook, as there's lots of information there, including lodging suggestions. It's also available as an E-book in Kindle, iBooks and other formats.