Flight
Baltimore/Washington International Thurgood Marshall Airport is definitely the closest, by a lot! Luckily, they service most airlines: Southwest, American, Spirit, Delta, United, Alaska, etc. Technically, you could also fly into Dulles or Reagan, but it could be a 2 hour drive to Baltimore if you hit DC traffic at the wrong time of day.
Train
Penn Station is centrally-located and is a popular pickup spot for taxis and Uber/Lyft rides. Amtrak is a great option if you're traveling from DC, NYC, or Boston!
Hotel
We do not have a specialty room rate at this hotel, but it is a solid option! It's about a 12-15 minute drive from the Cloisters and a 20-25 minute drive from Downtown Baltimore.
Hotel
John & Brittany have stayed here before & enjoyed it. As of late January, rooms are still available here for less than $100/night.