I agree with AlexKMG. You think your toddler will get bored, but it's actually you. Children always find something new or interesting or friends. The world is a playground.
I don't know if he's old enough, but the railway museum (don't know how good it is), may be interesting. He may want a train for his birthday though hahaha.
There's a place called "Baby Colour" on the 4th floor at Nan Ya Shopping Center (Dianchi Road at the big Thai gates, building entrance is opposite the McDonalds).
The owner (James) is from New Zealand/China and speaks also perfect English. They work on the artistic side with the children in very small classes. They have dedicated professional teachers who are very skilled. It's not that cheap, but the program spans a LOT of classes so it's actually quite good value if artistic skill is something you value. And they can take your boy off your hands for a while and maybe after a while you can go shopping or go for coffee and pick him up again.
(There are other baby art places on that floor, but I don't know how good their standards are. I know that education is priority in his book for sure. His place is close to the arcade).
I recommend the Golden Temple Park and bell-tower (next to the Expo Park). Tickets are not expensive if I remember correctly and it's really big, very pretty and with also many greenhouses containing a large variety of different plants and flowers. To see everything you need more than a day.
There is a "fish temple and park" (Heilongtan Fish Park) in Duanlongyuan which is quite cool and beautiful (about 1 hour north of Kunming). I'll have to add to the listings it as it's one of the prettiest and best parks I've been to with more than a 1000 fish you can feed. There are even some gigantic fish that look like sharks.
This whole area has great, super-clear fresh water, so the whole valley focusses on fruit trees (if I am correct) and a lot of fish-farms.
If you like fishing, there are various ponds you can pay a small fee to rent a rod and fish at. The fish you catch you can keep (pay per kg I think) and is as fresh as can be.
Please be very careful with your toddler if you're anywhere near water. The fish park is excellent though. Many families go there
for a nice day out.
The boulevard along Dianchi Lake (near the cable-lift) is also a nice walk and good for a bit of fresh air.
I saw a mini-golf near Dianchi Lake in the listings too.
If you need phone-numbers or addresses, just send me a private message and I'll send them to you.
Good luck and I'll post more ideas if I think of them.