One of the sites that I visit most on my phone is also one that works well on mobile. I wish I could be a little more original, but it’s Youtube. It’s not the best website I have ever seen, but it works well and gets the job done.
The hamburger menu on the top left corner works well. The search bar is the main part of the navigation. This makes sense considering most people would visit this site to search for a video they have already seen. Especially on the mobile version.
I think this site skips the frills and gets right to the point. I think it has a good approach to mobile design while keeping in mind the users needs.