Placement of RC filter used for slew rate limiting (for EMC)
So let's say you have a micro with signals feeding off to a connector.
  Should these filters go near the micro or the connector?


For most applications it doesn't matter, if the signals are +10MHz then parasitics will start to come into play. Run a PCB trace calculator and then analyze the schematic with the parastics drawn in. 


  As an example, i know if the RC was the other way around, R close to
  connector and C to ground after. That would imply they're being used
  for ESD (dealing with signal coming onto board as opposed to going
  out), and you would keep ESD components close to connector so they
  don't couple across to any other lines. Does this apply for EMC in any
  way?


A case where you would want to put an RC Filter or diodes is on a connector that comes into the board. The capacitor should be placed next to the connector to short out high frequency currents and send them to ground or back through the connector.

PCB traces have capacitance between layers of a few pF's. Signals can couple between layers, so keeping them short between the filter and connector reduces the chance of noise coupling to the board.