The mall has a large indoor play land for toddlers, and everything is rubberized so they can go nuts. It’s free, and a helluva lot more sane than Chuck E Cheese.
Our nearest mall has a pretty small indoor play land for toddlers - I’m guessing maybe a 40x20 oval. It’s certainly better than nothing, but it is kinda tricky to supervise him there. On the one hand, there really isn’t room for parents like me to hang too close to their kids, but on the other, he’s still at an age where he needs to be able to see Mommy or Daddy when he looks up and wonders where we are. He’s also at an age where he doesn’t really understand sharing and taking turns, so I need to be close enough to occasionally step in and make sure he gives way to a kid who’s playing with the thing that he wants to be playing with. So it’s a resource that I’ll use, but gotta admit I’m not exceedingly fond of it.
And the mall is a half hour away, which is kind of a long trip for something like that unless I’m going that way anyway, or unless I’m getting desperate. It’s just a function of living in an exurb, I expect: not much in the way of good indoor places to take your kid to, and a ways away to boot.
Fortunately, there’ve been a lot of good suggestions in this thread for things we can do in the house itself, and they’re inherently less location-dependent.
Wait, you don’t take turns? Turnabout is fair play, we started enforcing it because his grandmothers wanted to tickle the Kidlet without giving him a chance to tickle back. If someone tickles him, he can tickle back, and of course the recipient of the tickles is allowed to run away from the tickler. This also gave us the chance to teach him the difference between tickling, scratching and poking.
Do a geographically-restricted search on “bounce house.”
They get plenty of opportunity to attack. They usually come after me though, and leave daddy alone.
Where do you live?
We are lucky to have an Ikea close by - the kids treat this as a fun night out. They get to run around in the play area, we all have dinner and then the kids get cones while Mom and Dad drink coffee (and maybe have a cinnamon roll).
If we don’t buy anything else, this will usually set our family of five back around 25 bucks. Ikea runs their cafeteria and snack bar as loss leaders.
You have mentioned before that you are a bike rider - we had our kids in the bike trailer at that age. The trailer is nicely weatherproof, and is another fun thing to do.
That’s a great idea!
Northern Calvert County, MD.
The nearest IKEA to us, the one right off the Beltway in College Park, is probably about 45-50 minutes away. But I’d forgotten about their play area - it’s really quite good, IIRC, and I’d say it’s more worth the longer drive than the play area at our mall is worth the shorter one. Thanks for the suggestion!
That’s another of those instances where the advantages of being in an exurban environment turn into at least a perceived disadvantage. There’s a lot of good cycling around here, but unlike DC and northern VA, it’s all on public roads. I feel safe riding on them, but outside the mile or so of roads in our neighborhood, I’m a bit queasy about taking the Firebug in a trailer on them. That may be irrational, but aren’t we all. 
Stay in your neighborhood then. Those are the same streets the small one will ride with you when he gets his bike.
It is monotonous, I admit, riding around the same blocks all of the time - but kids don’t feel that kind of monotony when they’re on or around a bicycle. Besides, he’ll probably be telling you to go faster, so you won’t be bored for long. 
I was going to say “ride the bus” - but given your location maybe you don’t have one? Worth considering if you do.
Second, third and fourth norinew’s suggestion of a sink-full (well, half-full…) of bubbles. My Small Boy loves “doing the washing up”
Ever made playdough? Playdough is great. Lots of recipes on the intarwebs.
Play puppydogs. Throw the ball. He fetches the ball. Throw the ball. He fetches the ball… You get to sit down for that one!
Do bouncing rhymes (I do this with me lying in the middle of the bed. Even MORE relaxation for mummy!). These two are good for about half an hour…
Mother and father and uncle John
Rode to the market one by one
Mother fell OFF (fling him to one side)
Father fell OFF (other side)
But uncle John rode on and on and on and on and on…
This is the way the ladies ride (jiggity jig, jiggity jig)x2
This is the gentlemen ride (gallop a trop gallop a trot)x2
This is the way the farmer rides (THUMPETY THUMP THUMPETY THUMP)x2
And this is the way the butcher boy rides (over and over and over and OFF!)
I’ve heard that helium filled UFO shaped balloons are fun for the whole family!
It’s too soon … isn’t it? 
CMC fnord!
I just throw em outside and hope they go into hibernation till spring time. Doesnt always happen, but it at least always turns out I get a peaceful winter no matter what.
My toddler used to make “potions” - mix a little oil, vinegar, jelly, honey, corn syrup, salt, sugar, and everything from the spice rack - stir up with water, and voila, there’s yer potions.
Also, washing (plastic and unbreakable) dishes and cups and such, standing on a chair at the sink (under supervision, of course) took up a surprising amount of time. Washing toys in the bathtub - God knows, they needed it! Fingerpaints. Having a sockball fight (yeah, pairs of socks rolled up in balls) across the bed.