You can wear a brown suit at any event where the attire is "business casual" or even "smart casual." The color is inherently more casual than a dark worsted business suit in grey or navy, especially if the suit has a texture like tweed or corduroy.
In today's casual world, this is a good way to sneak in a more classic and always stylish outfit. With a brown suit, I recommend an oxford shirt in beige, cream, or striped blue. Avoid solid white with a tab collar, as that's more business-y. If you don't want to wear a tie with your brown suit, I recommend a camp collar shirt, maybe with the collar overtop the lapels of your jacket. Super cool!