Easily doable in one day (but would have been less rushed in 2).
Don't come here on a Saturday. There will be a lot of locals in addition to tourists.
It's worth spending the night in a nearby hotel the night before so that you don't have to attempt to figure out the Tokyo subway while you're half asleep.
Get here at least 30 mins to an hour before opening time. You may not be admitted into the park if you're late.
Grab a map from the main gate turnstile if you want something in English. There are folks wandering around with maps but they may be harder to find if you don't know who you're looking for.
There's an app for wait times you can download for iOS (it's made by TDR-- these folks) or go to TDRNOW.com
From the main gate, go left and over the bridge towards "New York." Get fast passes for Tower of Terror. (Most likely you will be caught in a huge rush of people who are pretty much running towards the Buzz Lightyear ride.)
See if you can score tickets for the big band show, but it's a lottery system so if you don't get them, you can either come back to wait in line, or you can skip it (like I did).
Go to the standby line for Journey to the Center of the Earth.
From here either go to Indiana Jones (either single rider or get fast passes if you can, similar to how the ride works in LA) or back to Tower of Terror.
After Tower of Terror you can go to the Teddy Roosevelt lounge. Highly recommended you walk to the upper decks of the ship and take in the view. You can either walk through Cape Cod or back through New York to get to Magellan's.
Just a bit past cape cod towards Adventureland is the stall that sells Donald's bun. It's quite good.
Go to Magellan's to see if you can get table service.
Walk to Sinbad and ride it (there isn't much of a line most of the time).
Eat Chandu's tail. They also have curry at the stall that sells the tails, and that was pretty decent too.
From there you can decide where you want to spend your time at the rest of the park. I personally enjoyed the playground around Magellan's and exploring the castle around the Magellan's restaurant. I also enjoyed wandering around all the different lands and marveling at the level of detail (particularly the back corner of Venice that has the gondolas, and the marketplaces/carousel near Sinbad). Ariel's grotto was definitely themed for little kids as was the Buzz Lightyear ride.
The stores are nice, they have a stationery store as well as lots of food and gifts. There is plenty of unique merchandise here that doesn't exist anywhere else.