First of all we ultimately won't be in heaven. We will inhabit a new creation with nations and commerce (Rev. 21 & 22). Beyond that there's not much sure detail that I know of.
Personally, I can't imagine God doing any less with the new one than He did with the old one. I think we'll live, evolve, and explore in it just like this one, only better since you know who (satan and his ilke) won't be around to screw it up.