A 2 year old isn't old enough to be able to fully communicate what he wants to do, or old enough to appreciate most tourist attractions, so you can still do nearly 100% of what Mum and Dad want to do.  I think he'd enjoy Disneyland Park (what kid wouldn't?) and the Los Angeles Zoo (toddlers love big animals). 

A beach day in Santa Barbara, Pismo Beach or Big Sur (all along PCH) is fun for the whole family.  A toddler might enjoy the sea otters, sharks and other sea creatures at Monterey Bay Aquarium.

San Francisco is a city for adults and not kids, but again a 2 year old isn't old enough to be affected by homeless people peeing out in the open streets, people shooting dope in alleys and aggressive LGBTs and other people of "alternative" lifestyles (which SF is full of) taunting people with overt displays of their lifestyles.  I've noticed that in general the locals in SF aren't too fond of children or too willing to accommodate them.

Chicago is a great city.  Navy Pier is kid friendly, and if you want to experience quintessential Americana catch a Cubs game at Wrigley Field.  The parklands along Lake Michigan make great picnic spots and many have playgrounds and rides for toddlers.

An ankle-biter would love the Bronx Zoo and the Statue of Liberty in NYC, but alas, FAO Schwarz (the famous ginormous toy store) closed its doors about a year ago :-( 

In Boston, a cruise in Boston Harbour to see the boats would be cool, as would a paddleboat ride in Boston Common.

In general,  you'll find the USA to be very accommodating to small children.  Hotels will offer cribs and rollaway beds, and many will offer to use their kitchens to heat bottles.  Restaurants often have kid-friendly choices on the menu and people are very accommodating to families with small children on airplanes and other forms of public transport.  Nappies ("diapers" in American English) are available everywhere and are very inexpensive.

I can help with the Chicago stop. Since you're looking at August, it could be hot but Chicago is great in the summer. With a 2-year-old toddler, the easiest thing is to explore a lot of the outdoors if the weather is nice.

The standard things will be The Bean, Millenium Park, and Navy Pier. If you don't mind your son getting wet, he might really enjoy the Crown Fountain with the wet pavement and faces on the video sculptures.

The other thing would be museums. Chicago really has world-class museums, so if the weather is too hot or you want a break from the outdoors, you can go to museum campus and check out the Field Museum of Natural History, Shedd Aquarium, or Adler Planetarium. If you are into biking yourself, you could see if you can have your kid sit in bike trailer and ride along the lakefront trail from museum campus up to the beaches.

I'm focusing mostly on the area downtown, Gold Coast, and the busier tourist areas since there's a lot to do within walking distance. I'd stay in a hotel right in the middle of the area if possible so you don't have to deal with long travel times with a kid, and you can get back to the hotel for a nap if necessary.

There are tons of restaurants, but it really depends on your kid. Chicago-style pizza is great for you. Your kid might enjoy the Rainforest Cafe if they're not scared of the thunder/lightning effects. In general, I'd pick a central area to stay where you can walk to restaurants, again it's just easier to keep things close together when you're getting around with a kid!

Oh, for the drive from LA to SF on PCH, there's a ton of great advice from Trippy members here.

The Chicago Children's Museum at Navy Pier is the perfect spot for you and your little guy. After you spend time there you can take a lake cruise, ride the ferris wheel, run through  a water attraction, and eat at either a great fast food restaurant in the court or Bubba Gump Shrimp Co or the DMK Burger Bar. All of you will have a great day!

Chicago has a great system of public parks with awesome, toddler-friendly playgrounds. You could take your 2-year-old to Millennium Park or to the playground at Maggie Daley Park if you're staying downtown. But check out neighborhoods like Lincoln Square Neighborhood for kid-friendly shops, restaurants, public square and parks like Welles Park. It's an easy trip on the brown line from downtown — and that train ride has great views of the city, too.

Free stuff for kids: The The Art Institute of Chicago has a free kids play/art room. Garfield Park Conservatory isn't in the greatest neighborhood but it's right off the train and beautiful/fun for kids. The Lincoln Park Zoo is probably the best free kids option.

Kid-friendly food: Most Italian restaurants (pizza!) in Chicago are super kid-friendly. Wishbone is close to downtown and very kid-friendly. 

Have fun!