The bowling club is the best choice because bowling is a lot of fun, and there is much rooma lot of space in a place like this, and most bowling clubs have access to food and drinks, which are appropriate for a birthday party.
In my opinion a barbecue isn't a good place to make a birthday party since there's a lot of smoke from the barbecue, it might start to rain, and over-allover all, bowling is more fun. The house could be a good place but why make a party at a house when you can go to a bowling alley? In my opinionI think a birthday party at the house is just boring.