Hi NoahsMama!
we are exactly the same as you, all Caleb has all day is ME and hes spirited, we do the same thing, just work around sleeps and feeds, I tried something more "set" but I just couldnt follow it, I got bored with it and I think he did too a little, but that was ages ago, i should try again now that hes a bit older.
some things about him that I have noticed that you may find too, is as PP said, they LOVE helping with the housework!even at 15 months Caleb helped me. So when I empty the rubbish bags, i give him the smaller ones from the bedroom or the toilet etc and tie a knot in it and take him to the big rubbish bin outside and let him drop it in. now all i have to do is leave the tied up bag outside the toilet door and he just picks it up, goes to the door, waits for me to open it and runs to the big bin outside. he loves helping give me the pegs when I hang out the washing. when I do some baking i give him his own bowl with a small amount of flour in it and a spoon, it makes a bit of a mess, but then so do I when i bake, but it keeps him out of my hair!
When we do the dishes, i make sure theres some tupperware for him to "wash" in the sink next to mine that I fill with a small amount of water, i pull up a chair and keep him close to me, he gets really wet so i tie a towel around him.
hmmmm, what else can I think of? we also go to music every thursday and playgroup every second wednesday, i try to see another person with a kid or have them over once a week too. these kids love being social.
I should also do more arts and crafts, i was thinking that this morning actually! we do have a chalk board with chalk that he likes and i also made some playdough but that doesnt really hold his interest that long