I took a cab to the theatre when I went last week and it was $10. There was a line of cabs waiting outside the station, and even though I was on a rush hour train, I didn't have any problem getting a cab. The cabbie I had gave me his card to call for a cab back, but I was staying with a friend and didn't need it. I would assume, however, that that's fairly standard practice.
The show is so wonderful, though, so I hope you enjoy it!
When I see the phrase "the ____ estate", I imagine a vast mansion in the country full of monocled men and high-collared women receiving letters about productions across the country and doing spit-takes at whatever they contain.
-Kad