You’re right. Usage of the colloquial phrase “a ways to go,” even if there’s an obvious grammatical contradiction between the plural noun “ways” and the singular article “a” that precedes it, seems to be widespread in some native-English-speaking countries. In fact, even the usually grammar-conscious Boston Globe used it in this headline of a February 3, 2008 story about President Barack Obama: “Stressing electability, Obama has a ways to go.”
You wouldn’t ever catch me using that phrase in my writing, though. It seems idiomatic, but the built-in grammatical contradiction in it calls too much attention to itself and is obviously stuff for needless distraction. I’d rather follow Paul Brian’s level-headed prescription in his book Common Errors in English where he says:
“In some dialects it’s common to say ‘You’ve got a ways to go before you’ve saved enough to buy a Miata,’ but in standard English it’s ‘a way to go.’”
Since you asked the question, though, I don’t think it’s advisable to say “I have ways to go”—without the article “a.” I’d rather that you say, “I have a way to go”—with the singular article “a” and the singular “way”—if you really mean that you need to do a lot of things first before achieving your goal, and, of course, if you don’t want to be bothered explaining what surely would be taken as quirkish grammar.