The best way that I have found for Travel between New York and Lancaster is to take the Greyhound bus between NY and Philly and then hop on the Amtrak train to Lancaster, or vice versa.
One way train tickets between Lancaster and Philly are $16 Saturdays, most of Sunday and Friday nights and $13 for the last Sunday ride, Friday mornings and all other weekdays. You can also get a 10% discount if you buy in advance with an ISIC card.
The Philly - NY train becomes rediculously expensive (something like $80) while the Greyhound is only $40 round trip and doesn't take much longer.
To get between the Amtrak and Greyhound stations in Philly, you must take the light rail two stops. Ask any attendents and they can tell you which direction. If you have an Amtrak ticket for that day you can ride for free between these stops.
In NY the bus picks/drops at the Port Authority and in Lancaster the Amtrack station is several blocks north of downtown on several local bus routes.
Yes - there is a "regional" airport, and you can rent a car there (you'll need one anyway). Compare costs and fly into Philadelphia, Harrisburg, or Baltimore, and rent a car. You can also take the rail from Philadelphia to Lancaster (Philadelphia's local Septa train to center city Philadelphia, then get Amtrak to Lancaster for about $20). You'll need to plan ahead regading a rental car; the local Amtrak station does not have onsite rentals. The train ride on Amtrak goes right through farm country, so that is a plus of using this option. If you're staying at the Hotel Brunswick in downtown Lancaster, it's only a 5 minute cab ride from the historic Amtrak station.
There's a mass transit bus service, Red Rose Transit (RRTA). The hub is in the city, so if you're staying in town, it might be "okay". But - seriously - if you want to see the best sights and make use of your time, make sure you have a car to get around in.
By Car : Philadelphia in about 65 miles from Lancaster. You can take I-76 West (Schuylkill Expressway) to US-202. US-202 West to US-30 West.
By Air : Lancaster Airport has flights from more than 200 destinations daily. There is car rental and ground transportation available.
Buggy Rides : There are buggy tours conducted by the Amish you can take around the countryside.
Lancaster County is great to drive through, but I imaging riding a bike would be even better if you're fit enough for it. Get a good map and plan your route. Some of the best towns to see are Lititz, Manheim, Ephrata and Intercourse and each of these is located off of Highway 772.
Be careful, because you will see Amish horse drawn carriages all over the county. Please pass them with caution.
Lancaster can be accessed by I-283 from Harrisburg, US 30 from York and Philadelphia areas, US 222 from Allentown and Reading areas. US 30 and US 222 are the major thoroughfares.
Stay off the main roads during the weekends. Car and Rail are the 2 major modes of transportation.