With 7 days you probably can only have two bases, and it may either be Zermatt OR the Berner-Oberland for mountains, but not both. Can't really do Zermatt as a day trip. Don't spend time in Zurich unless you absolutely need to (we had to stay one night because our flight home left at 6 am for example). So figure out if you HAVE to stay in Zurich either at the beginning or end ( we arrived at 11 pm on our delayed flight and still made the last train to Lucerne but that was cutting it a bit close).
You could start in Lucerne, which is worth at least 2-4 nights depending on how your timing ends up. For example, if you have to stay in Zurich your first night, you could be in Lucerne mid-morning easily, and then spend 2 nights with effectively 3 days there. If you arrive late, you'll want to add another day/night so you can enjoy the area.
In the BO region, agree that Wengen or Murren are the best places to stay. Consensus is views in Murren are the best, but Wengen is slightly easier to get in and out of by train and has a vibe that teens and kids sometimes prefer. It is also a bit larger and therefore has more accommodation options. Wengen is also a good place to stay to do the Mannlichen to Kleine-Scheidegg hike, which is awesome, flat and easy and should not be missed. The cable car to Mannlichen leaves from Wengen, then you return to wherever you are staying via train from Kleine Schiedegg. The funicular above Murren is also nice and you can hike down to Murren from the top.
Zermatt is also a great mountain destination with lots of summer hiking options and great views. Be aware, however, that the Matterhorn can be sort of shy and may hide behind clouds for the period that you are there.