Solution #1: Community Centres / Public Libraries
Solution #2: Cafe / Restaurant / Transportation Hubs
Solution #3: Local Data Plan - Tethering
Solution #4: Work Offline
This may not be something you want to hear, I know I didn’t (at first). When the internet goes down, close your laptop, take a breath and step back. This could be happening for a reason, who knows, maybe this is just the motivation you needed to stop working on your website and actually start writing content for it. There are so many aspects of my projects that I do not need internet access to complete. I use my time offline to really dial in and focus on content creation, graphic design and brainstorming. Check out this article that discusses ways to unplug from technology and live mindfully.
Sometimes the internet can be distracting, so use your time without it effectively. That way when the internet is back up, all you need to do is upload some files, then you can head for the beach.