Enviromain I wrote a good part of the Wikipedia article, which involved a lot of research on my part. The area where Hemisfair Park exists today was, in the 1960's, a blighted area consisting mostly of small wood framed houses and other smaller structures. In order to clear the area for the fair the city used federal urban renewal funds and eminent domain to aquire the property. Hard to imagine given the state of the city today, but in the late 50's early 60's the central city was not the tourism, convention and business center it its today.
I hope that clears this up. The two links below are great resources on HemisFair '68 from "The San Antonio Express-News" and the UTSA Library archives.
http://www.lib.utsa.edu/Archives/Guides/hemisfair/index.html
http://www.mysanantonio.com/visitors_guide...N.3014646e.html
There is also a 20th Anniversary special from 1988 from local ABC affiliate KSAT-TV on YouTube you might find interesting as well. The audio is weak (probably from a VHS home recording of the program) so you should listen to it using a headset. Part 2 discusses the neighborhood that existed there and the use of eminent domain to buy it.
Part 1
Part 2
Part 3