Media market is probably better than even the nominal Metro areas as defined.
Arbitron's Radio Market list fits my general notions of town sizes in practice, and helps explain why certain places of a given size don't have sports teams (or why a smaller one does). Average income also matters but that requires pulling together various sources.
Reno, my nearest city, is pretty small for a AAA league. Unfortunately no AA league is near, and the town was sick of single-A. So they stretched, and with a new downtown ballpark the attendance so far has been encouraging. I still think we need to wait 10 years to really judge. Anyway, Arbitron lists Reno as 124th. Wilkes Barre-Scranton comes in at 71st. A quick scan of the list doesn't reveal anywhere markedly smaller than Reno that has AAA. It's hard to compare exactly, because once you get out of Reno and Carson City there aren't a lot of population centers within 50 miles for fans to make the trek, while a place like Lehigh Valley (Allentown-Bethlehem) has much more of this to draw from. OTOH Reno does pull in conventions and vacationers, who are looking for things to do, to an extent Scranton probably doesn't.
Back to the question at hand, Fargo-Moorhead ranks #204. Rochester MN is #205 and suffers (as already mentioned) from the larger city likely drawing away from them more than it would contribute. St. Cloud is #218. Duluth is #205. Sioux Falls is not listed (an error maybe) but looks like would slot in around #175. Eau Claire is #237. Cedar Rapids is #206. Frustrating, really - aside from the Twin Cities the state and surrounding area does have these pockets of population but they are so far from each other (and divided by the Twin Cities in several cases) that there is no synergy among them. Too small even for AA, by my quick scan; probably several could be candidates for single-A Midwest League, indeed they have had teams in the past and I guess don't like the small-time atmosphere.