I've done the Tokyo run from both HND and NRT airports a number of times, HND being the easiest. With the monorail at the terminal, easy to get it into Hamamatsucho/Daimon and its quiet frequent. Once there even at those stations there are some great little restaurants and you can do some walking through the local streets. From here its 3 stops on the JNR will take you into Tokyo station and you can walk around there, one way across to the Palace or the other side of the station to Ginza.
As a big user of public transport, Tokyo can be the hardest if you haven't studied up and a mistake can consume a lot of travel time. To understand the different train lines/companies, including the fantastic private lines is almost an art in itself. The other point is if you get into Tokyo and it does go "bum up" and time becomes critical, its easy to grab a taxi back to HND.
HND to Tokyo with the time you have fine, but you wouldn't do it from NRT as even using the Keisei Express to get to Uedo is just under an hour each way.