Hi PNW CHef,
Ok, I'll throw in my 2 cents worth. First, there is an Amtrak Station at Angel Stadium in Anaheim (it's literally in the baseball stadium parking lot). I would wager there is bus transport from Disneyland to there. From there, you can take the train to Union Station downtown. Phillipe's is right across the street from the station. When you eat, try to get a seat in the "circus room" off to the side in the front-----they have neat old photos as well as classic train models. After that, you are in walking distance to both Chinatown and Olvera Street----both touristy but possibly worth a look. Back on the train and you're in Anaheim in less than an hour.
Around the stadium, you have plenty of eating choices. Some may require a taxi but you might inquire if your hotel has a local shuttle---many in the area do and will take you places for a nominal fee. Roadfood-wise, it really depends on what you want. In-n-Out is a chain, but they are not like the usual chain----food is made fresh at each location. Kids love it too. My suggestion (off the secret menu)--a Double Double Animal Style with well-done fries. There is one on Brookhurst in Anaheim and one on Harbor Bl. in Fullerton, both less than a few miles from D'Land.
For a more upscale burger experience there is the Catch in anaheim, a new location for an old restaurant. They are pretty much walking distance from the Anaheim Metrolink Station (the train station is on the east side of the stadium parking lot and the Catch is on the west side of the parking lot. Might be fun to go to Phillipe's for lunch and the Catch for dinner. They are more upscale but I don't see any reason why your daughter wouldn't enjoy the liveliness. They also have burgers and sandwiches but those are primarily at lunch, so if that's what you are looking for maybe it's another day's visit for lunch. They even have a Primanti Bros. style sandwich! There are half a dozen different burgers on the menu. I can highly vouch for their food---it's delicious.
Near the In-n-Out in Anaheim is an area known as "Little Arabia". Not far awayon the way to and from Disneyland, are two of my favorite place. On Ball Road, there is a strip mall that caters to a Middle Eastern clientele. Stop first at Zankou chicken, for the best rotisserie chicken you've ever had. Make sure you try the garlic sauce! Their shwarma is also delicious. They have the fast-food style ordering----place and pickup at the counter----but the food is definitely not fast food. Well worth a try. Once you are almost stuffed, walk next door to Sarkis Pastry. They have many different types of baklava as well as enough other delicious sweet items to keep your daughter happy. From there, it's less than 10 minutes back to Disneyland.
One other nearby place I can highly recommend is Johnny Reb's. It's allso less than 10 minutes from the Park. They are definitely Roadfood----it's a Southern Roadhouse. Very kid friendly and fun. Food is really good and they serve breakfast lunch and dinner. My favorites are the chicken fried steak, fried catfish and the smoked ribs. The greens and hush puppies are outstanding and beans excellent. They also will give you seconds on the sides if you ask. If by any chance it's near your daughter's birthday, let them know----so much the better. My daughter still loves to go there for her birthday!
Finally, if you do want another burger place that has some Mexican items, there is Varsity Burgers of Anaheim. Better than average burgers with some Mexican specialties. Worth trying if you have the time, but the other places I've listed are my first choices.
If you have any more questions, feel free to ask. I'll see what I can do do help suggest. And if you decide you have the time, I'd be happy to join you at one of the places----I'm only about 20 minutes from Disneyland. Enjoy!
600 S. Brookhurst
ANAHEIM, CA 92804 www.in-n-out.com
The Catch at Anaheim
2100 E. Katella Ave.
Anaheim, CA 92806
2424 W. Ball Rd. #S & T
(714) 229.2060 www.zankouchicken.com
2424 Ball Rd.
Anaheim, CA 92804
Johnny Reb's Southern Roadhouse
2940 East Chapman Avenue
Orange, CA 92869-3704
(714) 633-3369 www.johnnyrebs.com
Varsity Burgers of Anaheim
600 west lincoln ave
Anaheim, CA 92805
Philippe The Original
1001 N. Alameda St.
Los Angeles, CA 90012
(213) 628-3781 www.philippes.com/