I see a lot of brick-and-mortar businesses around me that don’t bother with a website, and if they have one it’s usually ancient. It seems like most of their activity is on social media, mainly Facebook.
Do you need a website or will a Facebook page suffice?
YES.
Facebook is NOT your website. They can cancel, delete, ban, or reallocate your page. Your website should integrate with your social media, not the other way around.
I will go further: when looking for local businesses, I will not go to ones that only have a Facebook page. The FB only businesses rarely seem to bother with a clear statement of opening hours and how to contact them.