So with minneapolis massage I'd get great benefit for the keyword "minneapolis massage". But for every other keyword, the infinity of long-tails, I'm at a disadvantage for
EXACTLY! This reasoning is why I strongly recommend a short, branded domain name as the primary URL. My preference is to compete with great content and SEO strategies rather then trying to purchase an assortment of keyword domain names. That tactic is primarily for those who lack the proper SEO knowledge, or who have deep pockets to create a solid web page for each domain name and properly redirect it to the main site.
If you found a very high traffic perfect match phrase, you could consider acquiring the domain name and trying a couple things, but overall your best bet is a solid primary domain.
You have the disadvantage of a long city name (Minneapolis) along with other variations (Twin Cities) used. I would suggest focusing more on the "Fitness" aspect and allowing your physical location and other factors to establish relevancy for the location. "WalkerFitness", "SunshineFitness" or whatever brand seems to fit you best.
When trying to brainstorm names, engage your current clients. Make a poll, take a survey, give out a prize to whomever picks the best name! The process can generate publicity for you "Free 1 hour massage + 1 month fitness membership".