One bowl Iowa won't play in is the Pinstripe bowl. The Big Ten has a rule they must take different teams in 8 years. Iowa did its duty in 2017 and does not have to go back.
Depends on where you look I have seen Mayo and the Quik Lane. I remember back in the day Jon Miller being adamant that Iowa would never play in Detroit. I don't think they ever will under the current bowl format, but this year is really going to test that.