8 hour layover Tokyo on a Sunday (later afternoon/evening)

Others have asked similar questions before, but I think my situation is specific enough I will try again.

I have an 8 hour layover in Tokyo this coming Sunday. I land at Narita at 3:25pm, and I fly out of Haneda at 11:30pm. I have never been to Japan before, and I would love to capitalize on this tiny chunk of time to experience one of the world's great metropolises.

I see my timeline as roughly:
3:25pm - Land at Narita
5:30pm - Leave Narita (conservative estimate to retrieve bag and pass customs)
~ ?
9:30pm - Arrive at Haneda to check in
11:30pm - Depart for my destination

I will have a smaller-sized, checked bag with me, and I can either take that with me on my foray into the city, or I can head straight to Haneda to stash the bag in a locker (I think the former is probably the more workable).

My ideal scenario here is to stop in one note-worthy district of Tokyo where I can bask in the energy of the city, get a sense of its history, and stop someplace tasty to eat.

Here are my questions:
1) Is my timeline bollox, or is this workable given my humble aspirations?
2) Given my starting and ending locations, as well as the day and time, is there an obvious great location for me to target?
3) In said area, is there a recommended noodle house to try?

Possibly relevant details:
* This has all been arranged on short notice
* I do not speak any Japanese
* I am open to considering a guide with a car (but I'm not sure it would be worth it, considering my circumstances)
* I am also open to checking out an area near Haneda if there is anything noteworthy to see or do, given my timeline.

Best Answer

That's an interesting challenge, and there's no obviously superior solution, but here's two options for what I would probably do in your shoes:

If you get through immigration fast and the train schedule lines up, take the JR Narita Express to Shibuya. The train takes about 75 min and runs hourly. At Shibuya station, take the Hachiko Exit and you'll end up at the most famous pedestrian crossing in Tokyo if not the world, with tons of neon and night time energy. There are also countless eating options here. Once you've had your fill, continue by JR Yamanote Line to Hamamatsucho (18 min, trains run every few min) and transfer to the Tokyo Monorail to Haneda (13 min plus waiting time on express, some services are slower). Alternatively, you can take the Yamanote to Shinagawa and continue with the Keikyu Airport train; this is marginally faster, but has none of the spectacular bayfront scenery you get from the elevated monorail.
If you're more crunched for time, take the Keisei Skyliner to Ueno, it runs more frequently and takes only 30 min. Ueno is a comparatively low-rent, more downkey hub, but it has its share of neon and plenty of eateries too. The Ameyoko arcade is right next to the station, and the Tenya fast-food tempura outlet here is the best meal you'll find in Tokyo for ¥500. From here, continue by JR Yamanote Line to Hamamatsucho (about 20 min) and take the Monorail.

In both cases, I would recommend traveling as light as humanly possible and not leaving your stuff in a locker, because both Ueno and Shibuya stations are huge and complicated: backtracking to the specific locker you used can be complicated and time-consuming. Also allow buffer time for navigating the stations, buying tickets, etc.

Also, while it's wise to leave buffer, you'll be unlikely to need more than one hour in NRT for immigration/baggage, and I feel pretty comfortable getting to HND one hour before international flights (although you'll want to get in earlier if you have to check in bags). So if your flights are on time, you'll probably have a fair bit of time. Don't get too hung up on eating at Shibuya/Ueno either, there are surprisingly decent eating options at HND itself.