While Wix is the Swiss Army knife of website builders (lots of features but looking a bit clunky), Squarespace is like a chef's knife (elegant, very focused).
All the templates look great on desktop and mobile and can be edited in depth with the style editor (each text, link or icon can be customized to look just the way you want). If that's not enough, you can jump in the CSS code and geek it out until the cows come home.
Unlike some competitors, Squarespace doesn't allow for backups.
There are also some great ecommerce features available, should you need to sell a few items through your website. Blogging is also available for all plans, and it's very polished.
There's no free plan but a 14 day free trial is available. Paid plans start at $12/month (for the yearly plan), which also includes a free domain.