I am wondering the same thing!! My little boy is 18 mo and we go to the library and to mommy/me classes at the YMCA. The difference between you and me is I live in WI - so in the winter, playing outdoors is really "weather permitting"!
One thing I do is have his toys kinda spread around the house...some in his bedroom, some in the living room, some in the basement (usually bigger toys like a bb hoop and balls, ride ons). We kinda travel around the house. We will play and do things in the living room, then I will put him in his high chair with some crayons while I make lunch, then quiet play in his room (books, puzzles, blocks) til nap, then after nap we go to the basement and run around (or go outside), etc. My son "helps" me a lot - which yours might be a little young yet, but Ben will hand me dishes from the dishwasher, push laundry baskets from room to room as I put clothes away, play with tupperware when I am cooking. If he isn't interested in the activity I am doing (folding laundry, etc.) he will entertain himself with something else nearby.
One thing I found that he absolutely LOVES is window crayons (crayola). We have a patio door and he LOVES drawing on the window with his crayons! They come off easy too.
I have also taken him to the pet stores to look at fish, birds, rodent pets...
Are there any "Mommy/Me" type classes? We do Gym at the Y and they have ideas that I bring home (soda bottle bowling, "hunting" like an easter egg hunt/gather but with seasonal items - put them out all over house and hunt, put in bucket, bean bag toss, etc.)
Good luck!!!!