Just Published: Theme Park Insider: 2016 Year in Review
If you have to go during Spring Break season, it'll be much more crowded, so be sure to get to the park first thing when it opens.
A tip - look at the calendar on the Disneyland website, and try to go on a day when the hours are shorter. If the park is open until Midnight, that means Disney knows it will be a busy day!
Days when the park closes at 8 are PERFECT for taking a 2-year-old. The park won't be crowded, and a toddler's not going to stay up late anyway. The only disadvantage is that there may not be a parade.
As for visiting with a two-year-old, I find that a tough age for visiting a theme park. The child likely won't remember much more than a image or two - the event is more for the parent or adult in the group. It can be fun, but you have to visit with no expectations whatsoever. A child might hate all the top attractions, but be absolutely enthralled watching a custodial cast member sweep up a sidewalk with a pan and broom - for 20 minutes. (That pretty well describes one Disneyland visit with my then-two-year-old son.)
That said, I have to recommend the most unique Disneyland attraction for a two-year-old. Go into the baby care center at the end of Main Street (behind the Corn Dog Wagon) and ask to use the potties. Back by the changing tables are a few porcelain toilets - scaled down to toddler size. Unlike other theme park toilets, not only are they potty-sized, they don't have automatic flush, either, so no on gets scared on them. My kids *loved* these when they were potty-training.
Walt Disney World
Tokyo Disney Resort