I found a good source on this.
http://www.gambling-law-us.com/State-Laws/
I'm pretty sure that games of skill are allowed by federal law so we only have to worry about the relevant states. I have looked up information for the assorted states and can confirm that, unless some lawyer really butchered these laws, smash tournaments for cash should be allowed in most states as long as you don't bet on other people's games. I also consider the elements of chance in smash bros to be sufficiently minor as to be ignorable for legal purposes via the commonly accepted standard that sports played for money are legal (football, for instance, starts with a coin flip). To be clear, I am NOT a lawyer in any way; I am reading the laws as written. Also, I am only looking at the states in the Midwest minus North and South Dakota (which have absolutely no known smash scene) and plus Kentucky, Oklahoma, and Texas which are significant to the Midwest smash scene.
Pretty definitely legal: Missouri, Kansas, Illinois, Minnesota, Wisconsin, Indiana, Ohio, Kentucky, Texas
Iowa's gambling laws are ridiculously opaque and obviously incredibly out of date. This is what I believe the section that may permit smash bros tournaments is section 99B.11. I believe you could consider a smash tournament a "similar contest, league, or tournament" under section 2d. It is clearly within the "spirit" of the law given section 2e. I can't say for sure our style of tournaments are legal in Iowa, but I think you'd have a good case.
Nebraska's gambling laws are super opaque too, but if I read it correctly, it seems to suggest that contests in which the prize depends on the number of entries (i.e. all smash tournaments) are illegal. Someone more familiar with the law might want to look into that.
Michigan state law is stupidly opaque and seems to make dumb things illegal if I read it right (like selling decks of cards or dice). It seems to bar pretty much any contest with a cash prize which would logically include smash bros tournaments, but maybe someone else should read over it.
I'm pretty sure Oklahoma's law is allowing it though it's not clear. It doesn't make a specific exception for skill based games, but it does define a bet as being chance based.
To sum it up, we have the following three categories (remembering that I'm not a lawyer):
Definitely legal: Missouri, Kansas, Illinois, Minnesota, Wisconsin, Indiana, Ohio, Kentucky, Texas
Probably legal: Iowa, Oklahoma
Seemingly illegal: Nebraska, Michigan
Further investigation would be welcome. I suggest people from other regions do similar research for their own regions. Of course, these laws are pretty much never going to be enforced on us; the bigger laws we would have to worry about would be tax evasion for tournament winnings. Still, it's good to know.