I think using TDL as your home base does make sense if the focus of your trip is on Disney.
First time visitors who are true Disney fans will probably want to spend 4 days in the parks. That will give you enough time to experience all attractions and take it all in without feeling rushed. Plus, starting from day 3 you can park hop

.
Now for an extra couple of days of sightseeing you could commute to the city quite easily. The only drawbacks are you probably wouldn't return to your hotel for an afternoon rest, and the commuting (about 30 mins each way).
But mind you, if you did a split stay you'd still have to commute once to the city (with all your bags) anyway, so that little bit of extra commuting is not a big deal in my opinion!
Now, the rooms at the Hilton Tokyo Bay and the Sheraton Tokyo Bay are much more spacious and offer far greater value than most hotels in this price range in the city. Especially for large families the value is extraordinary.
Another plus for people who don't speak Japanese (like myself) is that they know the Hilton and Sheraton inside the Disney Resort have English speaking staff with an excellent customer service guaranteed.
In short: If you spend 4 days at Disney and only 2 days in the city, I can highly recommend making Disney your home base!
Michael623, for your itinerary:
You'd arrive on Sunday and plan to visit the parks Monday-Thursday. May I recommend that after arriving in Tokyo, taking the friendly airport limosine bus (motorcoach) to the Sheraton and checking in, you take the Disney Monorail (5 Minutes) to Ikspiari? It is a shopping and entertainment area on Disney property. You could compare it to a more compact version of Downtown Disney with plenty of interesting places to see. If you feel a bit adventurous there are even a lot of good Japanese restaurants in there. You can also visit the "Bon Voyage" shop which is the largest
Disney Store in Japan. They offer different merchandise than inside the parks. Parts of Ikspiari is indoors so even on a rainy day it's worth to check it out. A visit could be as short as 1-2 hours or you could almost spend an entire day there...
Because you'd arrive on a Sunday (weekend), another option is buying the Starlight Passport to visit one of the theme parks on your arrival day. It is available from 3pm and the prices are:
Adult (Ages 18 & over) ¥4,900
Junior (Ages 12-17) ¥4,300
Child (Ages 11 & under) ¥3,400
However you will most likely be tired from the long flight and you will be spending the next 4 days in the parks anyway, so my personal recommendation is just exploring Ikspiari for a bit and then returning to the Sheraton early for a good nights sleep, so that you are fresh and energetic the next day for Disney.
Oh, since you will be changin planes in LA anyways, have you already considered the possibility of sneaking in a short trip to
Disneyland? If your airline ticket permits a free stopover this might be an opportunity to combine two Disney Resorts on one trip...
Best Regards,
Wuzefelix