Public library - story time, find a book and read it in a comfy chair, see if they have a small play area (ours has blocks, puppets, some small dress up things/costumes).
Children's museum or aquarium, if there's one near you. They often have "fenced" toddler play areas and hands-on exhibits. Get a toddler "leash" so he doesn't stray too far.
Large pet store - small amount of walking, put him in the stroller or the shopping cart, and look at the ferrets and guinea pigs and fish. It's free, the animals are protected from little hands, and there's a limited amount of walking. Most of them allow customers to bring their pets, so keep an eye out so your little one doesn't grab the ears of every dog walking by. The animal cages and fish tanks are usually stacked, so there is plenty at eye level even if he's in the shopping cart.
Fire house - unless there's a huge fire emergency, they are on standby, and usually happy to welcome kids. Our firefighters help lift the kids into the driver's seat of the engines, show them the ladders and helmets, etc. Over time, it helps build trust in the firefighters so kids don't run away from them.
Check local garden centers for free petting zoos or "just look/no pet" areas. We have several that welcome kids and have goats, turkeys, donkeys, sheep, chickens, etc. Some have food for purchase. Take a plastic container or cup with you and a bunch of quarters in case they only have the vending machines that dump out a handful of feed. If you have some ice cream cones, those are great for toddlers - it protects little fingers, and if the goat grabs it and eats it, it's not dangerous like a cup is. (One of our local zoos actually sells animal food in cones - that's where I got the idea.) Because the petting areas are small and there are only a few animals, it's not a 4 hour visit on your swollen pregnancy ankles!
Go to the thrift or children's resale shop and buy some inexpensive, used puzzles. Something new and exciting to occupy your toddler without a big outlay of cash.
Spread out a sheet on the family room floor and have a "picnic" with your regular lunch or snacks. Put a beach towel or old shower curtain underneath if you want to have drinks. Sit yourself near a chair so you can get back up by holding on!