Originally Posted by
MSPeconomist
Think also about airport transportation. IMO the most convenient is the Friendly airport limobus door to door to your hotel, from/to both HND and NRT, but you need to check the schedules carefully as some hotels have very frequent service while other (sometimes larger) hotels don't.
AFAIK, Ueno isn't on any airport bus routes. Fortunately, the Keisei railway offers good, direct, services from Narita - The Skyliner express fare is about Y2,400 with a journey time of about 40 minutes. The Limited Express fare is Y1,030 for a journey time of about 80 minutes.
From Haneda, the route to Ueno is a little more convoluted. You could take the monorail and transfer to the Yamanote line. As you say, it's not ideal if you have a lot of luggage.
Asakusa is well served with direct trains that go from both airports to Asakusa subway station, as Stut mentioned. These services depart from the Keisei station at Narita or Keikyu station at Haneda.
Definitely agree that you should not take the Narita Express via Tokyo station if you're heading to Ueno or Asakusa.