Here's a Q&A on the RNC put out by the NYPD.

Information includes a lengthy explanation of what's going on with Penn Station. It's the major train depot for the Long Island Railroad, Amtrak and several main subway arteries in the city and it sits right under Madison Square Garden - where the convention takes place.

Not only will it be open, but it will probably be the safest time ever to take mass transit. Says the NYPD:

Commuters should allow some extra time for their trip as every train will be inspected by law enforcement personnel prior to entering Penn Station.

And there will be many extra cops on duty (from several different agencies) during the show.