I personally didnt leave NY until I got both my contacts AND the essential skills to make it on my own when I do the cases in new cities.
Essential skills to have: Research, Footprint analysis, hand writing analysis, lock picking, advanced hair analysis, and advanced thread analysis. Since you're Tough: Adv Interrogation and Adv Intimidation.
Yeah, I know it's alot but better safe than sorry, right? >.>