Parents will always be a favorite play thing when they are around..
If I was doing things in the kitchen, sometimes, I would put our daughter in her high chair with toys to play with on the tray. Her high chair had wheels so I could push her around the house..
Playdo would be perfect.. I also had a handbag that she played with and I would put strange things in the bag and switch out the stuff.. She loved looking in it and putting stuff back in.. I would ask her to find a doll, a block, a blue thing.. etc..
Sometimes, I would have her "help me" wash dishes... I would give her some plastic stuff and a wash cloth with warm water and she would wipe them, then I would give her a dry wash cloth and tell her it is time to dry them..
Stacking cups, cars, blocks are all things that can be played in there..
When I did laundry, I would have her help me by having her hand me the clothes.. Hand her wet clothes to put in the dryer, take clothes out of the dryer, have her carry dry clothes to the living room, have her divide the clothes by mommies, daddies her clothes, the towels etc... Then we would 'fold' the clothes.. have her help me carry them to the bedrooms.. She had a toy grocery cart to help with all of the transporting..
Our daughter loved all things creative. Colors, washable markers, clay.
She also loved empty boxes, all sizes.. Sometimes we would leave them open on one side she would crawl or climb in and out of them, sometimes we would tape them all up so she could use them a huge blocks.. Sometimes, we let her color, paint or marker them.. Sometimes we would cut holes in them so she could make a tunnel in them..
I would allow her to take all of the pillows and Blankets into the living room and make tents.
Or I would give her 3 items have her hide them so that when dad came home, he would have to find them...
Our daughter loved Puzzles.. She would do them over and over.. I would then give her 2 and she would have to put them together at the same time.. deciding which pieces went with each puzzle.. As she outgrew the puzzles or became bored, I flipped the puzzle out (completed )and had her put the puzzle back together based on just the shapes..