Q. If the captain becomes incapacitated does the FO fly to an alternate airport, regardless of how close to the (Capt only landing) airport (and medics) they are ?
That's a judgement call Matt, and that's what pilot's are paid for by and large. You would need to take numerous factors into account. Being close to the restrictive airport may and often isn't the only variable. It probably is in a place like FNC because your alternates may now be further out of reach in terms of time.
Other variables will of course be weather, facilities available, time available (to descend, set up the aircraft and familiarise, brief yourself on a plan of action, consider fuel burn etc). You will be considering all this as single pilot, whilst at the same time dealing with ATC (having either made a Pan or Mayday call) while additionally having to deal with cabin crew/medical personnel attending to your incapacitated skipper.
In our network those restrictive airports (ie not only Captains only landing, but in terms of their location, type of approach available etc) I keep a few considerations to hand. A type of 'what would happen if...' type of scenario. Just like a Captain incapacitation. You could also apply it to any type of onboard medical emergency and indeed mechanical failure/malfunction. Time will always be a factor, however there are many other variables.
So back to your original question. I wouldn't totally regard the fact that an airfield is 'Captains only' as the primary deciding factor because your other options available at that moment in time may dictate a better course of action. However if the guys life is seriously under threat, you will need to get the aircraft on the ground as quickly but as safely as possible. This may equate to the restrictive aiport being your prime option. Some may argue that the risk you are taking here is that you are attempting a landing at an airfield where you, as an FO, are restricted from doing. Therefore you are placing everyone else at risk. However you try living with that when the coriner tells you that the captain proabably would have lived if you decided not to divert to a less restrictive airport. Now my airline doesn't operate to either INN or FNC, however considering the airports that we do operate to and which are 'Captain's only,' if I had little or no other option I would land. No question.