This is a tough one. Iowa has had some magical seasons tainted by disappointing bowl losses and some regular seasons not as great but that finished strong with big bow wins.
Magical seasons tainted by disappointing bowl losses
1985 - Iowa started 7-0 and was ranked #1 for 5 straight weeks. Includes classic win in #1 Iowa vs. #2 Michigan game. Outright Big Ten champions. Chuck Long was runner up in Heisman to Bo Jackson. Season Tainted by Rose Bowl loss to UCLA.
2002 - Iowa went 8-0 in Big Ten and 11-2 overall . Co- big ten champs. Including wins over MSU, PSU, Mich. Did not play OSU. QB Brad Banks was runner up in Heisman race to Carson Palmer. Tainted by Orange Bowl loss to USC.
2015 - Iowa started 12-0, went 8-0 in Big Ten and won the West. Lost Big Ten CCG to MSU 13-9. Tainted by Rose Bowl loss to Stanford.
2021 started out like a magical season, with Iowa starting 6-0, rising to #2 in the rankings with big wins over #19 Ind, #9 ISU and #4 PSU , but it was all a mirage, Iowa ended up 10-4. All those ranked teams Iowa beat ended up unranked in the end. Iowa's offense was exposed as just plain awful. Still somehow Iowa found a way to win the Big Ten West.
Magical Seasons with strong finishes
2004 - Iowa started 2-2, including a 44-7 loss to Arizona St, and was down to its 6th string RB when somehow Iowa finished 10-2 overall and was Big Ten co champs at 7-1. Included classic 6-4 win over PSU. Finished season with dramatic last second win in Cap One (citrus) bowl over Nick Saban and LSU.
2009 - Iowa started 9-0 with one improbable win after another. Blocking 2 FGs against UNI. Last second TD against MSU. A weird ping-pong pick 6 against Indiana. All ended when QB Ricky Stanzi got hurt against NW. In the defacto Big Ten championship game at OSU, Iowa's backup QB almost pulled out an upset, but Iowa lost in OT 27-24. Still Iowa rebounded and won the Orange Bowl with Ricky Stanzi back at QB. To finish 11-2.
I am going to have think about this. I am going to go with 1985. It truly was a special season despite the Rose Bowl loss.
But it was tempting to go with 2004 or 2009. Both seasons had bizarre, exciting, fun and unlikely wins topped off by big bowl wins.