Your daughter might like the Aquarium of the Pacific in Long Beach. They have four different climates so that allows them to have fish from different parts of the world. Not as big as the Monterey aquarium but it's still a very nice aquarium.
A visit to Jones Mini-Farm would be perfect for a 20 month old. That's in San Juan Capistrano, about a 30 - 35 mins. drive southwest of Anaheim. Pony rides, feeding farm animals. My kids like the corral/pen where the bunnies and guiena (sp?) pigs run around. You can enter the pen and pick them up. They also have a little train ride too. It's in a fairly small, compact area. In walking distance of that is the mission:something probably more of interest to you than a toddler if you like historical stuff. The mini farm is worth 1/2 - 1 hour of your time so if you're not interested in the mission, it may not be worth it to you to drive there.
An alternative is Irvine Regional Park. There are also pony rides and longer train ride there. It also houses a very small zoo, and I do mean SMALL! If you're coming before April 17th, you could also visit Green Meadows Children's Farm. It's a touring, educational farm that will be at Irivine Regional Park from now until April 17th. Very hands on experience feeding and petting a variety of farm animals. Also includes a pony ride, hay ride, and a chance to milk a cow!
As for Chinatown and Japan town; it's been a long time since I've been there (I grew up in L.A.). Chinatown isn't what it use to be because the hub of the Chinese community has moved to the Alhambra/Monterey Park area. Lots of shops and restaurants closed in Chinatown but I understand it's becoming a growing area for art galleries filling the abandoned shops. A lot of Chinese still shop there and it's still pretty congested so it's not so far removed from the busy Chinatown of old so it's still worth a visit. Olvera Street is close by, right next to Union Station, and is also worth a visit if you're in the area. It's one of the oldest streets in L.A. and is preserved like a street in a sleeply Mexican village might be. Very touristy but still interesting. Japan town is much smaller than Chinatown. Unless you're in search of good Japanese food or Japanese items, not really worth a visit.
For orchard picking, you'll probably have to drive to one of the surrounding counties like Riverside or San Bernadino. Developement has eaten up most of the farm land in Orange County. If you're still interested in driving out to an orchard, let me know what time of year you're planning your visit and I'll look up info for you in my book "Fun and Educational Places to go with Kids in Southern California".