Historically, Illinois’ biggest in conference rival is likely Indiana. This is likely a blind spot for PU fans given your own rivalry with them, but from Lou Henson feuding with Bob Knight to the Eric Gordon saga to the all-time series being almost even, that has been a great rivalry for decades.
Beyond that, Iowa has been an off-and-on rivalry that has gone from boiling (Deon Thomas/Bruce Pearl years) to stagnant (Lickliter years for them), but it’s REALLY heated back up these last two years. Lot of bad blood between the two, and we’re both good. Missouri is easily our biggest non-conference rival (and arguably the coolest non-conference setup in the sport, in St. Louis before Christmas in front of an evenly divided crowd at mid court), but a conference rivalry always seems to be more important.
UI certainly doesn’t have as natural of a rival as UM-MSU, IU-PU, UW-Minny, etc.