Planning a Switzerland trip – best base for Alps and budget?

Hi! I’m planning a 20-day trip to Europe in July with my brother and we’re trying to organize our itinerary 😊

We’ll be visiting Paris, Switzerland and Italy, but right now we’re focusing on Switzerland. We’re really interested in nature (Alps, hiking, lakes), and we’re thinking about places like Interlaken, Lauterbrunnen, a bit of Zurich, and maybe Bern if possible.

I’ve read that Interlaken is a good central base, but I’m not sure if it’s the best option or if there are better (and maybe cheaper) alternatives like Lauterbrunnen or Grindelwald.

Our goal is to have a great experience but not spend too much, so any advice on where to stay, what to prioritize, or what to skip would be really helpful 🙏

Also, we’re still figuring out Italy, so if anyone has recommendations (especially in northern Italy), I’d really appreciate it!

Thanks so much!