Despite the appearance, for once this is neither an abbreviation nor an acronym.
"Yourdictionary.com" has that to say:
Regional Note: The word spa, taken from the name of the famous mineral springs in Spa, Belgium, has become a common noun denoting any place with a medicinal or mineral spring. Less well known is its Eastern New England sense, "soda fountain," probably an allusion to the carbonated or "mineral" water that is a staple ingredient of many soda fountain concoctions.