score:2
Minneapolis native here.
MSP airport is less than 20 minutes from either city by car, so you could probably spend a few of your spare hours seeing a little of what there is to see and still have plenty of time to get back through airport security. I live in Southern California now, so I have experience with both MSP and LAX, and FWIW, the latter seems to have a much worse reputation for slow security check-in lines. I've never really had problems with either, personally β I always make it from ticket lobby to terminal in under a half hour.
Public transportation is available, but if you have more money to spare than time, taxi travel (or even car rental) might be wiser. Google seems to think you can get to St. Paul by bus about a half hour faster than to Minneapolis, but I've only been on a bus in the area once since I was a kid.
With regard to cost otherwise, what you want to see will matter more than which city it's in. The Twin Cities aren't so different that you'd expect to pick up on any substantial difference in what little time you'll have. Again, just FWIW, I have a very vague feeling that St. Paul might be marginally more expensive on the whole, but even after living in the metro area for 23 years, I don't feel confident in that judgment. They're twin cities in more than name alone.
If you're not sure what to do, consider a (very) quick buzz through the Minneapolis Institute of Arts. I find myself going back almost every time I visit my family, as they have cool traveling exhibits fairly often. Only those are ticketed; the rest is free, and includes pretty great Asian and African artifacts. If you prefer modern art, the Walker Art Center itself isn't free, but its iconic sculpture garden is.
(source: makefive.com) Kinda makes me hungry...
That skyline might be worth seeing in itself. It's my all-time favorite, but I'm probably biased...
If you don't like art, but the above made you hungry anyway, there's a bit more worth recommending. Both cities' menus are plenty eclectic. My friends like to pig out at Fogo de Chao (Brazilian steakhouse) in Minneapolis, but personally, I'm partial to Mirror of Korea and The Glockenspiel (German) in St. Paul.
Last, if after the first leg of your flight you've had enough of the follies of mankind, there's actually a nice little slice of nature to take in that's nearer to the airport than either city's heart: Minnehaha Falls... Surprisingly (even to me), that's just a 10-minute cab ride from the airport. Even so, this is all a bit much for a layover, so pick one or two at most, and call ahead if either is a restaurant.