R.W.
I used to just take my son to McDonald's and let him watch the older kids in the play area. Your son might be a bit too young for that, but if he does have any interest in watching other kids, McDonald's is a great indoor place to find them.
Also, Dynamoze is an indoor play area located in the shopping center at 281 and Brookhollow. They have a large matted area with big soft blocks for babies to play in. I believe it's even free for babies under 12 months.
From a very young age, my son liked to be anywhere where he could just watch people - and cars. I'd take him to a restaurant during off-hours, get myself a drink, set him up on the table and let him look out the window at cars going by on the freeway. He became very popular with the waitresses at the Denny's on Bitters and 281.
If you ever go to Houston, their children's museum has an EXCELLENT area for infants and toddlers. I have never seen another children's museum anywhere with such a great set-up for the tiniest tots. Don't bother with San Antonio's museum, and New Braunfels museum is probably too big for a 4 mo. But Houston must not be missed!