If you are interested, I would be more than happy to help you construct and host a website. It will cost you some money, but it's very cheap.

Edit: I didn't understand your post because I misread it.  Unfortunately, free website builders don't have a great user interface regarding accessibility.  If you're looking to just host podcasts, perhaps you should just distribute the Dropbox links instead of going through the hastle of uploading only a few links.  If you're definitely sure you want to go down the free route, I can give a few pointers:

1. Google Domains and website builder is fairly accessible.
2. Google, like other free website builders, includes its original domain name in your domain name.  You can get rid of it by simply paying the $12 assuming the domain name hasn't already been taken by any other service provider.
3. Wordpress is another option I'd recommend.  It's a blogging site, but it's a site that costs nothing.
4. If you are willing to shell out a few bucks every so often, you can host your own website.
5. If you choose to host your own website, website builders do not seem to be accessible.  (Somebody can jump in here).  You'll have to code the site with HTML and upload your HTML files to the host server.

Best regards,

Luke

I also have something called the awesome tech podcast at http://awesometech.samtupy.com whare you can upload podcasts to my website. I'll aprove them and then they'll be there, and each podcast get's an auto twitter tweat, so it's pretty much like the 2 services above but figured i'd throw it out there as another option.