I have found that the least expensive way to get to Tokyo is to use the Kensei Limited Express to Nippori Station. It is a station on the Yamanote Loop around Tokyo.
Here is the link for Narita Airport. It has information about the Kensei Limited Express.
I have stayed near Nippori Station at the Tokiwa Hotel. It is a buisness class hotel, and not a capsule hotel, but it does have a Onsen on the first floor, which is a very peticularly Japanese thing to have at a hotel. I am not sure this will work, but here is a link from JapaniCan:
http://www.japanican.com/hotels/shisetsudetail.aspx?ar=A27&sar=130309&...Oh, yeah. The last time I went, the vending machine in the hallway had Budweiser in it, along with the Japanese beers.
The capsule hotel is probably less than the hotel, but the cost to get to Nippori on the limited express will be less than going on the Narita Express. The costs will be close.
If this is still over your budget, and you want the Tatami mat experience. When you exit the Kensei side of Noppori Station, enter the JR side, and get on the JR Jordan line for two stops to Minami-Senju Station. This will cost you an 150 yen.
The Hotel New Azuma is not a capsule hotel, but almost. The room I stayed in was a three tatami mat room, which is a six by nine foot room, with a futon on the floor to sleep on. There is one shared bathroom on each floor, which will be designated for one sex, so you man have to go up or down one floor to go to the bathroom. The cost of this hotel is similar to a capsule hotel, but you are now in a tatami mat room, which is also unique to Japanese accomidations. I hope these hotel links are working:
http://www.japanican.com/hotels/accessmap.aspx?ar=A27&sar=130302&st=40... Another options is to take the Yamanote Loop to Ikebukuro, and stay at the Sakura Hotel, which is a International Hostel. There are dormitory rooms with several bunk beds in them, and you can sleep in one of these.
http://www.sakura-hotel.co.jp/ikebukuro/roomsThis is probably the least Japanese of the three options.