S.H.
I would really suggest... that you don't feel you "have to" entertain him, constantly. This is also not always beneficial.
Kids ALSO NEED time to themselves....where they are just playing by themselves, creatively and without constant "stimuli." This builds self-reliance and self-motivation... and creates a different kind of mastery in a child.
If one always "entertains" a child... they may also get used to it... and then can't think of anything by themselves or play by themselves.
Being "by yourself" is NOT a bad thing... it fosters quietude, reflection, thinking, peacefulness, concentration as well as many other things.
I think kids today,are "too" overly stimulated... meaning that as parents we feel we always have to "entertain" or be "teaching" our kids every second and turn them into little Einsteins or Mozarts, or make their aptitude into a 3 year old even though they are only 1-2 years old.
Just relax. Do your things... you can stay at home. And have him watch you too and what you do. That is what I do with my son who is 3, as well. I cook, clean, organize, read the paper etc... and ALL that time he is with me and I talk "out-loud" about what I am doing & thereby "teaching" him about life as he 'shadows' me around. He asks me questions about what I"m doing and about "life" and I teach him CONVERSATION skills as well as the experience of just "taking story with Mommy..." instead of lecturing/hovering/giving directions to him as a child. Which I feel is mega important. Sure, we also go out a lot and to the park and play dates and do errands. But, I don't "overly" entertain. There are times as well where I tell my son "can you play by yourself now... Mommy has to read the mail...", for example. And he says "okay, Mommy's turn..." and then he amused himself real well for his age.
BUT, things like this "teaches" a child TOO.
All the best,
Susan