Asakusa-Odaiba Direct Line connects Odaiba and Asakusa.
http://www.sunnypages.jp/travel_guide/tokyo_leisure/water_busses/Asakusa-Odaiba+Direct+Line/1875 Open new window
http://www.suijobus.co.jp/cruise/line/as_od_line.html

Odaiba (お台場 or simply Daiba 台場) is a popular newly-redeveloped waterfront area with the unique Fuji Television headquarter building (with a big globe inside), some shopping malls, parks, and a hotel.
http://www.japan-guide.com/e/e3008.html

Asakusa （浅草） is a popular traditional downtown Tokyo area with the famous Sensoji temple （浅草寺） (with the Kaminari-mon Gate 雷門 meaning Thunder Gate) and other temples & shrines.
http://www.japan-guide.com/e/e3004.html

Both areas are popular tourist spots, so I recommend that on a one day trip you move from one to the other using this Asakusa-Odaiba Direct Line, where you can enjoy the beautiful scenery along the Tokyo Bay water-front and the Sumida riverside areas including the Tokyo Skytree, the highest structure in Japan.
http://www.tokyo-skytree.jp/en/

This 50-60 minute one way trip is definitely worth the cost (1,520 yen for an adult, 910 yen for an elementary school pupil, and 300 yen for an infant of one year old or older), and you can enjoy both new and old Tokyo.