Join Date: Dec 2004
Location: Riding the rails
Programs: Japan Forum, Skyteam Elite Plus, BW Diamond Select, HHonors Gold, NWA, DL, NH
Posts: 1,936
The least expensive way would be the Keisei Limited Express at 1000yen into Ueno/Nippori Stations. From there you can connect to other JR lines to get to other places in Tokyo.
If you decide to stay around Asakusa, taking the Keisei Limited Express to Aoto Station, then changing to a local train that continues onto the Toei Asakusa Line to Asakusa is another option (1060yen).