Ha ha, I ask myself that every day! Especially now that the weather is so crappy and we're mostly housebound now. I want to entertain and stimulate my 4 month old, but I also don't want to overstimulate him or deprive him of the ability to entertain himself.
Plus he's such a catnapper during the day. I have a handful of activities we do every day, and he'll usually be cool for about 3 of those activities at a time before he's ready for another 45 minute nap.
I do sling him when I want to do chores like dishes and laundry, and he's extremely happy to just look around the house and then doze off when he gets sleepy.
He LOVES face time. So we will often just stare at each other making faces for a good 30 minutes at a time.
We have one of those baby gyms and also a mobile above his crib, but he gets fed up with it after 15 minutes or less. But for those 15 minutes it's a good activity and he can work on swatting and grabbing at toys swinging above him.
I do make an effort to do tummy time with him at least once a day. DS sort of hates it too, so I make sure to only do it when he's in a good mood -- then he's more willing to make the effort to lift his head and do a mini push up. One trick I learned recently is to put the crib mattress (if you have a crib) at a slight incline. Just put a pillow under the mattress. That makes it much easier for them to push up. But be careful, because when I did this the first time, DS rolled over from tummy to back almost immediately (after months of not being even close to doing this!) I wasn't prepared for that and he klonked his head a little bit against the crib railing. He wasn't too fazed though. After doing crib tummy time, DS was able to roll over on the floor no problem. And he seems to not hate floor tummy time as much any more. I think he just had to figure out that he had the skills and ability to roll over when he wants to.
Reading books is another activity we do a whole lot. DS is pretty patient and likes to sit on my lap while I read. He's become very grabby lately and will often shut the book or try to turn the pages, which is very cute. He's actually gotten pretty good at turning the pages on his board books.
Lately DS has become obsessed with his own hands and is much better at grasping things, so he is very entertained manipulating, holding, putting in his mouth a squeaky chew toy we have, and also a stuffed animal we have with all kinds of textures, rings, crinkly noises, etc. He also likes to watch me do stuff with my hands, so I'll often lay him on his back and do things like eensy weensy spider, patty cake, little bunny foo foo, etc.
Somehow our days are passing with all of these kinds of activities. It seems like every week he's got a new skill he's working on and we tend to focus on that skill for a week or so until he's moved on to a new one. I also think there's nothing wrong with just putting him in a chair or sling and letting him watch what's going on around him. If they're happy to sit there and watch you fold clothes, tidy up the house, do yoga, play the guitar etc, I think that can be very educational for them.
I personally try to avoid the TV, or wait until he's napping and watch stuff on my computer with headphones on. Besides the fact that it's supposedly not great for babies to watch TV, I'm worried that he might get to the point where he's ONLY interested in watching TV and doesn't have the attention span to do anything else (like watch me make faces at him for 30 minutes straight).
