Activities to do with a two-and-a-half-year-old?
Building tents/forts in the house with sheets/sofa cushions etc., then running in and out of them
"You're getting warmer/colder," wherein you hide some little thing and the little one hunts for it with clues from you.
If more than 2 of you, pussy in the corner.
Dancing (and falling down), recommend Frank Zappa, or Roll Over Beethoven. I bet there are also videos for this (it's been a long time since mine were 2 and we were stuck inside)
Plain old hide and seek?
Some of these will work inside: https://activeforlife.com/49-fun-physical-activities-to-do-with-kids-aged-2-to-4/
Blowing bubbles - encourages peaceful breathing and a little running around. Recommended for bathroom or basement, though....
I definitely sympathize with the 
! but breathe deeply yourself, and try to imagine this will eventually be a happy memory?
eta, you can do hopscotch, or whatever agility thing your little one is up to, with tape on the rug/floor : )
A two and a half year old I know likes being read to, especially books about dinosaurs; and drawing "pictures" using crayons on typing paper. Playing with toy cars and doing puzzles are other favorites.
for active play:
sing and dance. are there favorite videos? re enact them.
do you have balloons...play volleyball..let kid sit and bounce on the bed, you sit on chair a few feet away.
pretend play...it is so important, yet many kids don't get exposed to it much...for example, a kid into Thomas the Tank can make up stories for Thomas...pretend you are on a space ship or boat. build a fort with couch cushions.
turn empty bottles into bowling pins, toss bean bags at them....or just roll up socks to toss.
make paper airplanes... toss them into a laundry basket
make an obstacle course, put tape on the floor to jump from spot to spot, crawl under dining room table, bust through a cushion fort, etc...you can put a flag at the end of each (think Double Dare from nickelodeon....but not so messy.)
paint with shaving cream (on a table)
if you have rice, create a rice bin and hide small (but not too small) toys inside, have scoopers, cups, etc to play with
make a paper boat and sail it in the kitchen sink (maybe use coated box/cardboard or aluminum foil)
what does he normally do during the day? is he in daycare? can you contact them and ask about some favorite active play activities they have done inside?
if you can get one, a toddler trampoline with handlebar
Depending on how much of a mess you’re willing to tolerate, corn starch and water. If you can still find corn starch, that is. The consistency is such that they love playing with it, and after it dries you can actually vacuum it up pretty easily
Recreational baths. Was one of my standbys in the old days in the winter.
Find/make/order bath toys (or any waterproof creative props) and hang out.
Finger painting inside of a heavy duty ziplog bag. Put a small canvass and paints in the bag and let him paint away.
Looking for ideas for activities to do with an energetic two-and-a-half-year-old, especially when the weather is rainy or cold, and we're stuck indoors. Long days, long weeks.