Heard that HND is much closer to Tokyo than NRT. Therefore it's easier to get into town. Is that true?
An Australian comparison of HND vs NRT, in terms of distance from the city, would be AVV vs MEL.
Which airport is "better" depends on where in Tokyo you are trying to go or what sort of connection you are making.
Haneda is to the South East of Tokyo between Tokyo and Yokohama on the shore of Tokyo Bay. It is 15 minutes train from the nearest major station (Shinagawa).
Narita is about 50kms east of Tokyo in farm land in Chiba Prefecture. It is 38 minutes by high speed train from the North Eastern parts of Tokyo (Ueno). The JR "Express" (which many people think is the fastest option from Narita) takes 60 mins direct to Tokyo Station.
Both airports are connected to each other by bus and train options within 45-90 minutes depending transport method used and traffic conditions.
Haneda is "better" for the southern parts of Tokyo, while Narita can be "better" for the northern parts. Narita has a curfew, while Haneda doesn't. Narita has better international connections, while Haneda has better domestic connections.
It is no harder to get into Tokyo from NRT then from HND. Both airports have a number of train and bus options to locations all over the city.
Claiming that one Tokyo airport is "better" then the other is a non starter.