Given you have kids 6-7...
... and you have 3-4 extra days aside from Disneyland... I say, why even leave LA? You could go over to Knotts Berry Farm for 1 or even 2 days. Then - if your kids are speed freaks on the amusment park rides - then you might consider Magic Mountian in Valencia. That's perhaps 40 miles north of Disneyland. Also, you have a huge stretch of beach all the way north/west and south of you. Why not spend a day at or near the beach? The entire west coast is peppered with unique beach communities - with varying appeal for your family. Below are a couple images of my daughter flying a kite for the 1st time from Seaward Beach in Malibu...
I might suggest places like Balboa Island in OC, or if your kids are into surfing - then it's Huntington Beach for a simple surf environment; or there are (the last time I checked) stretches of Huntington beach with fire pits. Have a bon fire in the early evening and do marshmellos, hotdogs or ??? what ever is your fancy from a local market. DO keep to your self as you get all sorts on the beach at nite. COntinuing northwards - you could hang out in Long Beach. They have a nice aquarium (The Aquarium of the Pacific), plus Pikes Place with a Spielberg Gameworks, theaters and a smattering of fair to decent restuarants - plus a lot of walking areas. The Aquarium is an educational experience too.
ALSO... right there in Long Beach (as well as in Newport Beach and San Pedro) are docks where you can hop a high speed ferry to Catalina Island. This is a humble - almost modest experience. Yet still - if has merit for those who understand what to expect from a trip like this. You can rent electric carts and explore, ride a semi-submersible submarine, ride horses, rent a power boat and explore the shore, and so on. You see - Catalina offers a unique Pacific experience that is unlike anything else in LA/OC - while retaining a humble profile and modest intensity. IE - going to Catalina ia not going to be a saturating experience like doing Disneyland for a day.
North of Long Beach I'd consider Redondo Beach pier and the surrounding area. It is the furthest drive off the freeway - but it has some modest appeal with the pier. Then all the way north from redondo beach is a bike path that is mostly on the beach (it crosses onto city streets around Washington - some moderate traffic - you need to be careful - or it would be safer to just rent bikes and ride from Washington to the northern extreme near Pacific Pallisades). I fact - this is not so bad as there is a ton to see - it's all safe except for the hazard of crashing into other cyclists or into the sand... which is not all that bad. ANd in Venice - you have street vendors - wierd locals - muscle beach (see photo)
with lots of young folks and so on. AND just north of Venice/Manhatten Beach is Santa Monica. They have a pier there with simple low intensity attractions. My favorite being a guy who is pretty much a vagrant who operates a bubble blowing machine. He is really very charming and seems to be so kind to all the young kids chasing his bubbles.
Following a day at any of these things - you have an incredible wealth of dining options that span the entire rainbow of tastes and budgets. What did you expect with a 10-15 million population community. You could end up on restuarant row at Lawry's Prime RIb (one of my favorites) or Ruth Chris' steak house (yeah - I like the sizzlin' garlic butter presentation better then Mortons' plastic wrapped presentation). Or even the Stinkin' Rose across the street from Lawry's is memorable. Or - if snuggling with fameous movie personalities is your thing - then check out the blogs on what seems popular in Beverly Hills and Hollywood. OR - let me suggest the worn out but still relatively fameous Spago's or Palms.
OR - if your kids will find interest in enlightening diversons then - why not spend a day at the Getty Museum at the sepulveda pass off the 405? Or any number of other museums scatterred across town? You can take your pick from the Tar Pits, fine arts museums, Peterson Automotive museum, and so on.
OR... how about just going to Chinatown or (even better) Monterey Park or Alhambra for lobster and a banquet? There is a Vietnamese community in Westminister with lots of culturally rich restuarants too. OR - near Hollywood is Thai-town. There are lots of charming "hole in the wall" places there.
And while you're in Hollywood - how about going to the Hollywood Bowl for a concert if you're visiting from August through September? Tickets are reasonable and it will soak up your evening from 6PM til 11PM (getting in and out). If going on the weekdays then the bowl never sells out all 17,000 seats - so I would recommend buying the CHEAPEST seats while asking the box office where they are selling the best seats ... and just go in and sit BEHIND the area where they are selling the best seats. That area is likely unsold - and you can pay maybe $5-8 and sit in a $25-40 section. I bought my seats early for 4 concerts and my tickets range from $1~6 among the 84 tickets I bought! I go to the bowl with lots of friends, neighbors and our bible study group. OR - there are numerous small stages - with the best IMHO eing the Mark Taper at the Dorothy Chandler Pavillon. This tend to be more refined culturally - so if your kids tolerate that kind of stuff then this would be great. You can get HOT TICKETS about 90-120 minutes before curtin at cut rates. I think it used to be $5 for whatever they had unsold. You HAVE TO BE among the 1st few in line to guarantee seats at these cut rates. AND - medium to small stages are scatterred all over the LA/OC area. Mark Taper is the most refined IMHO.
Oh yeah... what about the LA Zoo or Universal Studios and the City walk up there? What about going to a Dodger or Angels game? Or any other pro sporting event - depending on what suits your fancy? TO get an impression of what may be going on - try a key word search on Ebay for the month and region within LA/OC that interests you?
Now - bear in mind - all thses things I've suggested more or less are not high profile diversions.... like you may find in San Diego. Like Sea World, SD Zoo, or Legoland. Well - I think legoland is really low profile still. But my point... there is A LOT to do in LA/OC. You could easily spend a lifetime exploring the things I've mentionsed here and still would not scratch the surface of what we've got out here. AND by the same token - many things I've mentioned MAY NOT BE very enjoiable to some. Everyone has their likes and dislikes - plus expectations and minimal needs. So - you need to approach this (obviously) with an appreciation for the preferen ces of your family.
ANYWAY.... before you leave Anaheim - consider what ELSE you're leaving behind in the greater LA/OC region. The scale of what you COULD do remaining in the area you're in - is only limited by your imagination, tolerance and ambition!