Nothing in the U district proper is springing to mind as worth a recommendation for Italian.
Within very easy cycling distance (less than a mile or so) are:
A bit to the north (slight hill) is Bella Rosa Bistro: 3410 NE 55th St.
A bit to the west (basically flat) is Bizarro Cafe in Wallingford: 1307 N 46th St
A bit to the south (downhill then slight uphill home) are Serafina (my favorite, but $$) at 2043 Eastlake Ave E or Pomodoro Ristorante at 2366 Eastlake Ave E.
A budget conscious choice might be Romios Pizza ad Pasta at 3242 Eastlake Ave E - just across the bridge from the U District.