What is a website I can play minecraft on for free?

Look up minecraft cracked version

The answer to both parts of your question are: No.

1. Is there a website where I can play Minecraft without a download?
--No, Minecraft requires a download. It isn't a large download, but it can't be played purely from a website.

2. I need it to be free?
--No. There's no way to legally play Minecraft for free, it is a product you have to purchase. And most of the sites that claim that they will give it to you for free will happily try to download viruses, spyware, and other things onto your computer when you go to them. Oh, and the survey pages are all phishing scams.