What are the best free online marketing tools?

I am afraid you need to ask the NEW GENERATION for this... :-))

I am just another oldie hahahahahahaha

it depend Which marketing :

For email marketing I suggest you Mailchimp

For keyword research I suggest you adword keyword planner

To target your free audiance of facebook you can use facebook audiance insight

to now they purchase behaviours

If you want to work with free traffic by trending event you can use google trends

the is some from a lot of free you can use to grow you business in the beginning