I would like to own a plantation.  I grew up on one when I was younger. 
You could probably make good money with the crops you could grow, like coffee or tea or sugar cane as well as cotton.
Are plantations usually big? 
Usually and the plantation houses, especially in the South were quite grand and expensive architectural works.
How much do plantations cost? 
I'm not sure of an exact cost, a lot though. Industrial plantations were established to produce a high volume of wood in a short amount of time. You have many options
Are plantations even existing in North America anymore? 
There are a few, but like every economic activity, it has changed over time
It might be best to purchase one outside of America then. 
That' s a good thought since protectionist policies and natural comparative advantage have sometimes contributed to where plantations can be located