I've been to both parks several times and most recently a year ago. I'd also strongly recommend Disney Sea over Tokyo Disneyland, which feels a bit like the Magic Kingdom at WDW. It's still got a bit of an 80's feel from when it was first built. Of course, growing up in SoCA and working at Disneyland, I'm probably a bit biased. That said, my one "must do" attraction at TDL is Winnie the Pooh. Best Pooh ride out of all the parks.
Keep in mind that rides you are used to in Anaheim and/or WDW are distributed among the parks in Tokyo so not everything at DisneySea is completely unheard of in the US. That said, they are certainly better representations in most cases.
It's a bit of a haul from Shinagawa (where Strings is located) to Disneyland in the morning. You'll transit through Tokyo station with that crazy long walk underground with a million other commuters.
Have you considered heading directly to the parks upon arrival in Tokyo? I did that a couple of times and actually made it in time to use the after 6pm ticket. Even if you choose not to spend the night there, you can do both parks in one day by using the evening ticket if available instead of purchasing another full, one-day ticket.