I have a layover in Tokyo from 8 AM to 6 PM. I plan on making my way into the city during that time and will be traveling light. This will be my first time in Tokyo, so where's the first place I should head to after landing? Just putting this out there, but I'm pretty adventurous and will eat anything!
Tough situation ... it will take you a good two hours to get from Narita Airport to anyplace fun in Tokyo. I'd say get as close to Akihabara as you can and just walk around. There is no place on earth crammed with as much wondrous stuff to gawk at per linear foot. Seriously.
Just so happens I wrote an answer to this question for a friend a while back, so I'll just repost it here. Forgive the length, probably more than you were asking for.
For a great intro to Tokyo, I'd suggest taking the JR Narita Express (N'EX) to Shibuya. It'll be about $40 round trip if you use this special http://www.jreast.co.jp/e/pass/nex_oneway.html, and takes 75 minutes. Shibuya's a pretty big station with a ton of exits, but the one you're looking for is called the Hachikō Exit, When you walk out of that exit, you'll see this HUGE intersection that goes like 7 ways, and when the lights turn, it fills with mad numbers of people going every direction. Featured in lots of movies, including Lost in Translation. Head through that intersection toward the gigantic neon signs, directly away from the exit, and that will put you in the main part of the neighborhood. I'd say just explore around there for a couple of hours, it's super cool. Tons of awesome little shops, restaurants, and cafes. If you're ready to explore, head up the main drag, called Dogenzaka; you'll pass the 109 building on the right as you go up the hill. If you duck into the tiny streets to the right a few blocks up, you'll be on "love hotel hill", which is an interesting area to check out, especially at night (and it's totally safe, just like pretty much all of Japan). If you should happen to spot the Tower records building in your wanderings, do yourself a favor and get a bowl of ramen at Ichiran, which is about half a block toward the station from Tower. *Incredibly delicious* ramen, and a fun dining experience- vending machines, tiny private booths, etc. (If not, more ramen below.)
The next stop I'd recommend is Harajuku, which is one station away from Shibuya on the Yamanote line. From Harajuku station, walk into Yoyogi Park (it's right behind the station) and have a stroll through Meiji Shrine; it's quite lovely. Walk back out of the park, staying on the left side, head down the hill on Omotesando-- it's an upscale shopping street down the hill from the station. If you're hungry, one of the better ramen shops in the area, Kyushu Jangara Ramen, is right there. really easy to find, just walk down the hill from the station on left side of the main boulevard (Omotesando) and look to your left after you pass under the first foot bridge. It's the red place, second floor. get the tonkotsu ramen with special pork and soft boiled egg. Unbelievably delicious with a nama biiru (literally, 'fresh beer' - unpasteurized malty goodness) http://modernyeti.tumblr.com/post/103443721688/kyushu-jangara
After the ramen place, continue down the hill and after 3 or 4 blocks, take a left at the VW bus-turned-cafe. Walk that way a couple of blocks to Takeshita Street (street) It's the epicenter of Harajuku street style, with all the cosplay and crazy lolita/goth kids. Amazing people watching here, too.
When you're ready, if the weather's nice, I'd recommend actually walking back to Shibuya to catch the train back to Narita. It's an easy 15-20 minute walk through some nice little areas. From Takeshita Dori, head back to Omotesando and cross over to the opposite side, if you want some souvenirs, definitely stop at Kiddy Land-- several floors of seriously awesome toys and beyond. Best souvenirs ever. Continue a little further up Omotesando and keep an eye out to the right; there's a very nice pedestrian-only street that will take you straight back into Shibuya. Even accounting for getting a little lost, all of this shouldn't take more than 4-5 hours.
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Shinjuku is a more modern neighborhood with malls, brand shops and restaurants, but the crossing from "Lost in Translation" is there and it's quite impressive to see
Hope it helps & enjoy your day in Tokyo!