I have two different passes for you to consider. First, is the Swiss Pass. Unlimited travel throughout Switzerland except for some high mountain tops (i.e. Jungfrau, Schilthorn) where you get a 50% discount. Full travel coverage includes travel to the mountain villages of the Lauterbrunnen Valley (Grindelwald, Wengen, Gimmelwald and Muerren). This pass is priced in 4, 8, 15, 22-day (and higher) variations. The 15-day per person price for two for the Swiss Saver pass is CHF387 (AUD401).
Second is the Swiss 1/2-fare card. It costs CHF99 (AUD103) and is good for 30 days. Very simply, it provides a 50% discount on all Swiss transportation. You might have to pay a reservation fee on the William Tell Express. With ours, we had to pay this fee for the Glacier Express.
Since you are traveling in May/June, some information on the Alps in the Lauterbrunnen Valley. Most of the higher villages close in April/May for "shoulder season". This is when they are closing down winter and getting ready for summer. Who closes when and who doesn't varies. The closure dates vary as well. We were in the area in very early June. The snow was gone through 6,000' and the weather was great although this can vary as well. Muerren was quiet and just coming alive from their shutdown. You could easily travel to any of the villages.
A couple of suggestions for the Lauterbrunnen Valley in very early June. 1) we stayed at the Hotel Silberhorn in Lauterbrunnen. Muerren is smaller but stunning if you wish to stay there but we really enjoyed the Silberhorn. A tad more expensive but the best restaurant/food in the valley. 2) the wildflowers are in full bloom. Take the very easy downhill walk from Muerren to Gimmelwald. Wildflowers and fabulous views to whole way. 3) most every morning, farmers are walking their Swiss cows with those melodious Swiss cow bells through towns up to summer pasture. Just some ideas.