I recently got a chromebook, and I've been brainstorming different ways to put mediawiki on it (with localhost, not a server). One way I've read about online is to go into developer mode to download and set up LAMP. I was wondering, wouldn't I be able to store the apache, mysql, php, and mediawiki files on the cloud (google drive)? And if so, would anything prevent me from accessing my wiki on any other computer's localhost, assuming I could just log into Google Drive to access these files? Might there be any reduced performance when operating from the cloud?
As others have pointed out, Google Drive (or another cloud file store/virtual drive) is not going to work well for what you are proposing.
Web servers don't have to cost. For example, I run IIS on my Windows desktop PC at home for my personal sites/webapps, and have for many years now. Costs nothing beyond the usual ISP and power bills.
Also, not sure about where you are, but many/most ISPs around here include a small amount of web space to each of their customers. Perhaps call you ISP and see what they offer.
Additionally Microsoft's Azure claims to give you up to 10 web sites for free: