In WebWave, you can build mobile optimized websites with any graphic design without coding for free. There is a huge selection of free templates, but you can also start with a blank page. It is also a great e-commerce tool.
Premium Plan costs 7$/month and allows you to publish the website under your own domain name. I believe there is a discount for new users, who get Premium Plan for 3$/month and a domain for free for a whole year.