Well son, (good) Nose Tackles come from the first two rounds of the draft!
I collected up some NTs most would consider at least "good" and looked at where they were drafted.
A few came late but the sample leans heavily towards the first day of the draft.Vince Wilfork NE
Casey Hampton PIT
Kris Jenkins NY
Shaun Rogers CLE
Jamal Williams DEN
Kelly Gregg BAL
Jay Ratliff DAL
This sample has an mean draft position of 3.2. Looks like if KC wants to lock up a nose tackle then day 1 is the time to get it done.