First things first: Lyndon Johnson had very little, if anything, to do with the site selection for what was then called the Manned Space Center. The selection of the current location of what is now known as the Johnson Space Center was made in September 1961, over two years before President Kennedy was assassinated. It was a very common ploy in those days for a presidential candidate to choose a highly ranked opponent from that candidate's own party as one's running mate. The intent was to put that opponent in a meaningless/powerless job that the opponent could nonetheless not refuse.
NASA appointed a site selection committee to evaluate candidate sites. The criteria submitted to Congress included
- Access to water transport by large barges,
- A moderate climate,
- Availability of all-weather commercial jet service,
- A well-established industrial complex with supporting technical facilities and labor,
- Close proximity to a culturally attractive community in the vicinity of an institution of higher education,
- A strong electric utility and water supply,
- At least 1,000 acres of land, and
- Low cost to the government.
The committee initially selected nine sites. The site where Johnson Space Center is located was not on that initial list. (A Houston site was on the list, but it was a tens of miles away from JSC's location.) Politics most certainly did play a hand in this. That initial list of nine sites was quickly expanded to 23 thanks to political intervention.
One of those political interventions was by Olin Teague, then the representative of Texas' 6th Congressional District. He (and others) convinced Rice University to donate 1620 acres of land to NASA for the purposes of putting humans (or at the time, men) into space. The land would revert to Rice as soon as NASA stopped using it for this purpose. Per the selection committee's checklist, this vaulted that site to the second spot on their list. No other political intervention came close to this.
The first choice on the committee's list was MacDill Air Force Base near Tampa, Florida. The Air Force had been planning on shuttering this base. This made that site extremely attractive. It strongly hit every bullet on the checklist, and the cost was essentially non-existent. But then the Air Force decided not to close the base after all. (MacDill remains an Air Force base to this day.) That pushed the number two choice to the top position.
What about what is now known as the Kennedy Space Center? That site was never on the committee's list. It failed on several criteria. One of the key reasons Cape Canaveral was chosen as a launch site was that it was far removed from civilization at that time. What is now known as KSC was run at that time from Marshall Space Flight Center as one of its remote sites. The site on the list that was closest to the Cape was Jacksonville, Florida, and it too suffered from "close proximity to a culturally attractive community in the vicinity of an institution of higher education." Higher education in northern Florida at that time meant trade school education beyond high school.
What about the criteria themselves? A canal had to be cut to make the site where JSC is located to make that site viable. As far as I can tell, that canal has never been used for the intended purpose. That Houston qualified as having a moderate climate Boston didn't seems to be a stretch. Perhaps one of committee members didn't like his wintertime work assignments in Boston? The other criteria make eminent sense.