Disclaimer: not sure this is the right place for this kind of question, sorry in advance, just point me to the right place and I'll move it.
In godaddy when paying only for domain, without hosting, they state you can get one page hosting for free but that option only opens their web-builder. I want to create a nicely design landing page, where the content is static.Is there a way to make my domain point to a wordpress one page or self created html one page/ landing page?
What GoDaddy is giving you, is a static, HTML only, webpage. A "business card" page basically. If you want dynamic content you need script access (Wordpress == PHP) and you need a real hosting plan for that. Once you have that, you can install wordpress and point your domain to it, using GoDaddy's webinterface .
Checking GoDaddy's Website Builder documentation, I see that they allow you to make custom edits to the page CSS. That alone should go a long way in helping you design a custom static page. You might also experiment with '@import' URLs in your CSS, which would let you grab further assets they may not support. Depends on how much functionality they allow really.
Another option is to point your domain to Tumblr and customise it there instead. I've done this and it works very well, with a great deal of customisation possible.
If you really must use Wordpress for a simple one-pager then you can point your domain there as well, though they charge you $13/year for the privilege.
