Here's my own take to this:

Where do you find inspiration and ideas to start a new project?

• Do you have interests outside of webdev? Is there a project you can make based on that? E.g. You really like music, how about making a website where you can create playlists using Youtube URLs?
• Is there something you feel is missing in your life and the tools that are out there aren't satisfying you? E.g. You want an easier way to send articles to your e-reader, so you create a Chrome extension that does exactly that (I actually did that!)
• Look at your friends and other communities you're in, or even social media. Make something you think will benefit others! E.g. Some of your friends own a snake pet, how about making a tool for them that uses their smartphone to closely monitor the terrarium?

Most of us devs aren't exactly good at designing. How do you go around that?

I... I don't. I'd like to get better at designing but I do feel my skills are at least up there to know how to put things together from a UX/UI standpoint! The best advice I can give here is to learn some basics through courses and books.

If this is solely for your portfolio, I wouldn't get too worried about your project looking ugly! Dev recruiters can look past this. Otherwise, if you really don't have time or motivation to learn some design principles yourself, find a designer to collaborate with!