Arriving at Narita Aiport at 10:15pm

Hey, I'm arriving at Narita Airport on American Airlines at 10:15pm (American Airlines) on Wednesday next week.
I know that JR rail lines to Tokyo will be closed by then (and the office to get my pass) and I probably won't even be able to make the last local train to Narita which leaves at 11pm. I plan to stay at a hotel in Narita for the night, but and I'm assuming I will exit the airport after 11pm. Therefore, do I have any option to get to my hotel in Narita other than taking a very expensive taxi? (How much would a taxi even cost?)

Thanks for your help!

No, you don't arrive at Narita Airport. You arrive at Haneda Airport!

About Haneda:
http://www.japan-guide.com/e/e2430.html

^ Yes, I just discovered my crucial error today. Now that the airport is more convenient, do you have any recommendations of cheap, yet good quality hotels or hostels to stay for the first night in central Tokyo?

There are several hotels around Shinagawa Station, easily accessed in a direct train ride from Haneda.

he Keikyu EX Inn and Shinagawa Prince offer good value rooms:
http://www.japanican.com/hotels/shisetsudetail.aspx?st=4013084&ref=EXJ...
http://www.agoda.com/asia/japan/tokyo/shinagawa_prince_hotel_main_towe...

I'm just a college student/backpacker on a two week trip, so those hotels are a bit out of budget for me, but thank you anyways!

Unless you flight has a major delay, a 22:15 arrival should still allow you to reach most places in Tokyo before trains stop running. I recommend the following service for low budget accommodation:
http://www.hostelworld.com/