Indeed, converting CO2 to some hydrocarbon is subject to a lot of research, but it is energetically "uphill". Plants do it remarkably well, I always wonder how these articial systems compare with just having more plant in the same volume of space. The key is to take plants once fully grown and "entomb" them so they don't rot.
A tree basically is composed of water, CO2, combined with sunlight and time (and some minors). They are quite amazing, and some trees like eucalyptus grow very rapidly in the right climate.
I like trees and have wondered if it would make sense to plant more trees along Interstate highways on the rights of way far enough from traffic to be no hazard. Of course, that could make it hard to see the billboards.