The Armed Forces Bowl is Army v. Big Ten this year. I'm not sure whether there's a backup conference if Army isn't bowl eligible or if there are not enough eligible Big Ten schools.
I'd say there's a decent chance BYU plays in the Armed Forces Bowl. Frankly, that's not a bad landing spot, whether against the Big Ten or Army.
Also the AAC owns the Miami Beach bowl and has a spot in the Hawaii Bowl. I could see the AAC try to broker a deal to get BYU in Miami or Hawaii - especially if BYU has a good year - depending on how many AAC, CUSA, and MWC schools are bowl eligible and who gets the G5's NY6 bid.
Either of those are better than the other bowls that are likely to be available, again depending on how many MWC and CUSA schools are bowl eligible:
- New Mexico Bowl (MWC v. CUSA)
- Arizona Bowl (in Tucson) (MWC v. CUSA)
- Famous Idaho Potato Bowl (MWC v. MAC)
Of these 3, I'd probably prefer the Arizona Bowl. We already play half of the MWC, so I'd cross my fingers for a bowl against Air Force, CSU, or SDSU.