MBB Chicago vs NYC --> PE

Few comments:

• I'd say no material difference in placements as Chicago and New York are viewed as similar "tier" of offices in terms of competitiveness of MBB hiring --> In the recruiting process, I simply focus on the fact that it's MBB (i.e., Tier 1 consulting) rather than any emphasis on specific office (with limited exception for "easier" offices to get into, but even then)
• The only tiny difference is if you specifically want NY PE (versus SF, Chicago, LA, etc.), those working in NY will be able to visit firms a bit easier for coffee chats and superdays but that's a minor logistical nuance and not worth inverting your lifestyle/impending job over one week of future interviews IMO
• Finally, switching to another office is actually not that easy and NY is typically the most sought after office (perhaps globally)