I use Weebly for my website, but I'm using it for more than just comics (I just promote it like I do my other works and then try to make people read it on tapastic - I feel like the comic I'm doing right now doesn't need it's own website, but I have other projects that might do).
The thing I can say about weebly is that you have quite a few themes to chose from, so it's not unthinkable that you could find something that works well for comics, I just personally haven't looked for it, and if you know some coding you can make changes to the themes. I think weekly are relatively cheap, I've never had any issues with them, and I think the designs are easy to customise - even without knowing coding. You don't have to pay to use it - if I remember correctly, you only have to start paying if you want your own domain. So you can build your website and try out different themes without worrying about money. I have two other unpublished websites through weebly that I'm still working on, and they're not costing me anything.
But like @Kaykedrawsthings said, there's Wordpress, and though I haven't used Wordpress myself, I know there's a ton of themes to chose from, and it's popular for a reason.
Tumblr has a comic theme too: Simple Webcomic Theme. I think it looks pretty good actually, and it's relatively customisable, you have to try it out to really see what you can do with it. Since it's through tumblr it has it's limits of course, but then again you could have your work reblogged endlessly if it gets picked up by the right people...
