I've used jQuery Mobile a few times now and it strikes me as a library that is excellent to use if you're trying to build a mobile web application. Something that will loosely resemble a native application.
For websites however, it would not be my first port of call.
Your question is relatively broad... the "best" tool is usually the tool that gets the job done with a minimum amount of fuss and a maximum amount of flexibility (IMHO).
When we're talking about a mobile site, there are many possibilities and scenarios, depending on the type of website we're talking about.
If it's a relatively content driven website, you might be better off simply using a responsive framework such as
If you've got a website that is functioning like a tool, or a web application, you could try one of the following:
- Sencha Touch