If you can afford it, don't move directly into the city, check out Yonkers. If you have to, I'd recommend the N. Bronx, a lot of Irish there and it is easy enough to escape the city if you need to.
Check out Riverdale, Pelham Parkway, Fordham University area and Italian Belmont. The rent is a lot cheaper in the Bronx and it is safe.
You might want to try and find a roommate. Try doing some networking and you might be able to find another Irish immigrant. Always make sure you request a background check on the individual and interview them to make sure they'll fit with your personality. As with everything, get a contract (legal and binding) for any roommates so they can't stiff you rent and utilities.
I'm not too up on the bar scene anymore, it changes yearly. Rory Dolans is a good place, lots of Irish, cops and firefighters (it is in Yonkers).
How come you're moving to NYC? That's a very expensive place to start off. Have you thought about other cities? I know NYC has a lure, but it can be a very hard and cold life for someone just starting out and if you have the option to go elsewhere, it would be cheaper, safer and easier than jumping head first into the larger cities.