I think the answer to this question depends on your child and what they are into. My kids are 7 and 3 now, both of them were in Disneyworld at age 2. We're DVC members so we spent most of our time at Old Key West, but we did spend some time at resorts. Almost all the resorts are kid-friendly, but each offers different things that will appeal to different kids.
Like others have said, Port Orleans is a really nice resort and very kid-friendly. We stayed in the "Alligator Bayou" section of Riverside because they have pull-out trundle beds (on floor under bed) which work well for young kids. The food court is great and the pools are nice (although the main pool is pretty busy). We have been pretty far away from the food court, not necessarily a bad thing for an active kid who likes to walk (or ride in a stroller). The only problem we ran into was skinned knees - some of the paths have slight hills, and my daughter liked to run full steam... and then she'd lose it and fall. She left Riverside with band-aids on both knees!
Riverside has a great playground too, although you'll have to watch a 2-year-old carefully as parts of it are fairly challenging. We've spent the ends of some days at that playground, letting our kids blow off some steam.
French Quarter is also nice... young kids like the cool themes and bright colors. The slide is awesome if your kid is adventurous in the water. It's a small, gentle slide. 2 is pretty young, though... my son is 3 now and I think he is just now ready for that slide.
Caribbean Beach is also an option... while it's not my favorite resort by any stretch, the cool pirate theming appeals to some kids. It's also a bright, cheerful resort and very kid-friendly. (Too kid friendly for my tastes - there are usually a lot of kids there, and it can get a little loud.) You can get stuck in Siberia in that resort too, so be sure to make a request to be near the front.
Any of the Value Resorts would work, but I'd recommend All-Star Movies if you can get in. They have a Toy Story section that is just awesome - a GIANT Buzz Lightyear, etc. My kids were just totally BLOWN AWAY by it. On our next trip (October) we plan to go visit that section just for something fun for the kids to do! I've never been to Pop Century, but I'd imagine the theming would go over the heads of younger kids - maybe others can offer their thoughts on this...
I'd steer away from Coronado - in my opinion, it's not quite as kid friendly because of the business theme, and the food court is much more expensive.
Last thought... if you want to cough up a few extra $$$, consider the Wilderness Lodge. Depending on discounts, you might be able to get a woods view for roughly the cost of a moderate. It's VERY kid friendly, with bedtime story telling at night, arcade, walking paths, GREAT restaurant where they let the kids run amok with play "horses" during dinner, good playground and a beach. But here's the best part... you can catch a BOAT to Magic Kingdom! With a 2-year-old, you'll be spending a lot of time in the Magic Kingdom. This way, you can take the boat and avoid dealing with all the buses. The boat ride is really enjoyable for kids and adults alike. You can also ride the boat to the Contemporary (which has a great arcade, Chef Mickey's (good character breakfast!) and access to the monorail) or to Fort Wilderness (which has an AWESOME petting zoo your 2-year-old would love, as well as a good buffet dinner that is very kid-friendly. FW also has Hoop-de-doo review, but that was a little loud for my 2-year-old: "Hoop-de-doo, Hoop-de-doo, my little kid hated Hoop-de-doo!")
Feel free to e-mail me with any questions -
pax_65@yahoo.com. We've definitely done the Disney experience with 2-year-olds!
Good luck!
Jon