CharlesRyan
Adventurer
The key thing in a few people's stories, though, is that running a game with a baby really requires running in the house of that baby.
To be clear, I don't think this is necessarily true in the case of an infant. We gamed at our friends' houses all the time when our first child was less than 6 months old. They're pretty portable, they spend a fair amount of time sleeping, and they're immobile--spread a blanket on the floor and give them a few toys, and you're good to go.
Once they hit about 6 months of age, and can sit up and scoot around, your problems multiply and you probably will need to play at the parents' home.