The places where you come across the cows and goats on hikes depends on when you go there. I think they gradually graze their way up higher in the alpine mountains as the summer progresses and the weather warms up in the higher areas.
Mürren has a swimming pool in their recreation center, which also houses the Tourist Information center (Tourismus). There's an amazing, fun playground at Allmendhubel, which is a funicular ride above Mürren. It has a stunning mountain view. There's also an interesting playground at Winteregg, an easy walk or train ride (one stop) from Mürren. Or take the train from Mürren, since you're staying there, and get off the train at Grütschalp. From there, take the easy walk to Winteregg with the mountains in your view. After playing in the playground at the cafe there, take the train from there back to Mürren (or walk from there on to Mürren).
On the other side of the valley, Wengen has a playground, and Männlichen (a cable car ride up above Wengen) has a great playground, including a rustic child-size bowling alley with a view of the spectacular snow-capped mountain range. If your children can hike 2 1/2 miles, there's a fairly easy hike from that playground (take the colorful little slide, or the steps, down from the playground to the hiking trail) to Kleine Scheidegg. As the hike ends, the Grindelwaldblick restaurant at Kleine Scheidegg has a swing set and a lookout tower to climb up to. (Also has great food and great view.) On that same hike (from Männlichen to Kleine Scheidegg), about 2/3 of the way to the end, there's a look out area that has lots of benches for stopping to take a break there, snack and enjoy the view. There are also benches all along the way.
If you take the easy path down from Kleine Scheidegg to Wengernalp, which starts across the train tracks and roughly parallels it, (It's about 2 to 3 miles long) you'll walk through a cow-grazing pasture. Houses and huts sell cheese just past there, with signs that say, "Käse zu Verkaufen" (Cheese for Sale). Or you can take the train to Wengernalp and, from there, walk down under the train track and follow the signs to Wixi, right by there, to find the cheese huts and cows nearby.
Train passes cost the same price in Swiss francs whether you buy them in advance or at the Swiss train station when you need them. Although the passes that apply throughout the whole of Switzerland (Swiss Travel Pass, Swiss Travel Pass Flex, Half Fare Card) are available at train stations and Tourist Information (Tourismus) offices all over Switzerland, you can only buy the Berner Oberland Regional Pass at train stations and Tourist Info offices that are in the region where it's valid, so in your case, the first place you'll find it for sale, on your way to Mürren from Basel, is in the Bern train station. (Or you can buy it in advance on the internet.) You'll have to do the math, pricing how much is covered by each kind of pass with your own itinerary to know which pass is best for you.
