Is there parking there?

parking is not easy in Manhattan, the cathedral is in a very busy area, it is advisable to use the metro or public transport, or just walk.

No. Use the metro, public transport, just walk, Uber or Lyft.

Parking is very difficult take the bus or subway

Two blocks from the cathedral there is a parking building. It's expensive but I think there is not other alternative.

I would strongly encourage against it. If you are staying anywhere in or near Manhattan, take the subway. It'll be way easier and convenient. It is not a far walk from Grand Central on 42nd, there are parking decks, but it is very expensive and difficult to drive a car in Midtown Manhattan without some serious prior planning, unless you wanna try to get in and see the cathedral only.

I recommend you use public transport if you want to visit the Cathedral.

parking garages nearby. cars not easy in city.