Definitely follow AlwaysAisle's advice and go straight to HND first to drop off the bags. If you want to explore Tokyo a bit and this is your first time in Tokyo, then forget trying to save money by taking some commuter train while carrying around luggage. In fact, forget about NEx because that means getting off at Shinagawa and then transferring to the commuter-style Keikyu train at Shinagawa most likely around 5.30~6p. I recently took that Keikyu train with suitcases in tow in the evening... it was brutal. So I would just do the easiest thing, which would be to take the bus straight from NRT to HND. See the schedule here:
http://www.limousinebus.co.jp/en/pla...ches/index/3/3

You won't have that much time. But if you decide to head to Shinjuku or Shibuya, you'll still probably have close to 3hours. For Shinjuku/Shibuya, you're best off taking Monorail to Tennozu Isle and then transferring to Saikyo line. You should return back the way you came and plan on leaving Shinjuku by 10pm in order to get back to HND for your midnight flight.