On walks:
Tell simple stories - Goldilocks, Billy Goats Gruff, The Enormous Turnip, even modern day children's books that you've read enough to know by heart, like 'Peace at Last' or 'We're going on a Bear Hunt' - toddlers like repetition, and will be enthralled if you're animated - you can even match the motion of the buggy to the tempo of the story, so when you reach a scary climax you start to run etc
Have a 'treasure hunt'. You don't need to make it complicated, though you can print out pictures of things to find on a laminated card, or look for physical things like a feather or a pinecone that you can take home if you want to. For everyday though just tell him 3 things you want to spot on your walk - 'I'm looking for a red postbox and a black cat and a man on a bicycle'... If they're old enough you can then ask them what 3 things they want to spot too. You can keep up a running commentary about it as you power walk along, 'Oh look THERE'S a cat! I was looking for a cat! But he's orange with white stripes, and I'm looking for a BLACK cat! What does a cat say?' blah blah blah
Sing songs. Yes you'll feel like a total twat marching along the street singing 'Ten green bottles' and 'The wheels on the bus' but who cares?! It'll keep him occupied and will actually end up being fun for you too!
At the playground, run around together. Take a ball or pocket kite, or get into pretend play, being a monster chasing him, or a pirate on a ship in a storm, or a princess on the back of a flying dragon, etc etc. You can kill an hour at the park this way, even in dodgy weather if you invest in some waterproofs.
Dance together! On wet days I like to have a 'living room disco' with the kids, curtains drawn, flashing Christmas lights draped around, cheesy pop cranked up. You can burn off some serious calories and it's fun too.
Set up an obstacle course with a folding indoor slide, cushions to jump from one to the next, a tunnel to crawl through etc. You might be too big to join in but it should be fun enough that it keeps him busy while you do a quick HIIT workout or whatever.
If you have a garden, challenge yourself to a beep test (you can find one on Youtube and play it on your phone) while keeping an eye on him as he plays out there.
Get a toddler seat for your bike and go on some adventures. I like those ones where they sit in front of you because you can talk about everything they see.