I live in Switzerland and the Berner Oberland is my favourite part! In terms of cable cars, we often buy a one way ticket and then find a hiking route down the mountain, which is an easy way to hike with kids too.
Its worth checking specific lifts as some offer an afternoon ticket which is cheaper. Also, just in case it’s your birthday, some offer free tickets for the birthday person (such as the Niesen which is nearby to Adelboden).
in terms of Adelboden itself, the Engstligen falls are really impressive - they are the second highest in CH. you can park at the bottom and it’s a short hike up to see them. You can also hike up to the top. There’s also a cable car which you can take to the top and there’s a really nice flat 5km circular hike at the top (but would advise hiking 1km down to see the top of the falls up close). The cable car is pretty reasonable cost wise compared to others.
Nearby is Oeschinensee which you can access from Kandersteg. There’s the choice of shorter hike down to the lake, or a longer circular loop which gives amazing views (8.5km). It is stunning but I’d advise avoiding it on a weekend day as it can get very busy.
There is also the Allmenalp cable car on the opposite side of the valley which is cheaper and also gives great views - and a choice of hikes from there too.
This is a good hike from Adelboden centre
https://adelboden-lenk-kandersteg.ch/en/activities/tour/detail/adelboden-cholerenschlucht-retour-1
Fuel is currently around 1.80/1.85chf per litre
Feel free to message me if you need any more info, happy to help if I can, I know the area pretty well