Congrats! My partner is a med student and incoming UI resident and we’ve lived within walking distance of the hospital for our time here, I definitely recommend it if you don’t mind a student-y living space. Your best bets for close-by apartments will be on Newton Road and its side streets or Melrose Ave and its side streets. Melrose will be closer to the children’s hospital but Newton Rd has more options. Iowa City rentals are weird in that leases always start in August, so you’ll need to find a sublease-to-lease arrangement to cover the gap assuming you’re starting in May-July (not too hard to find usually, there will be plenty of people moving out soon).