Sardines. One person hides, the others look for them and each has to squeeze into the space the original hider is in once the hider is found. I think this is usually done with the lights off, but not with a three year old. paper games where each has a long strip of paper, everyone draws a head, folds it down so it cannot be seen and passes on to the next person who draws the arms and the folding down and passing on continues until the person is complete. Unfold and there are lots of silly people. A 3 year old will probably need help.
We have lots of simple board games we play, Flounders, Scaredy Cat, a bagatelle game. look at the Early Learning Centre stock of games. Choose games the child will enjoy and up tosix people can play.
There is a start, I am sure you will get many more suggestions.