Hi. I have a 4 year old daughter. Here are some of her favorite at home things to do:
Playdough--she seriously plays with this for hours! If I have time I even let her help me make the homemade kind(Kool-aid playdough is my fav...) She loves to use cookie cutters and some of the play dough tools you can buy.
Forts--I let her use the cusions in the family room and blankets to make forts. She loves to take animals in there and use her flashlight and pretend she is camping. My 1 1/2 year old loves this too.
Animals-- Those little hard animals from Michaels and A C Moore are great! Just about every 4 year old I know, boys and girls, love these. They spark a lot of creativity alone or with other kids.
Art--drawing, painting, cutting, pasting, stensils, etc! You can give a 4 year old some glue, paper and alphabet pasta and let them get messy. It's so great to see what they come up with.
These are just some ideas--I know every kid is soooo different. I can't wait to see some of the other responses so I can get some new ideas too!