If you travel for good barbecue, head out to Sheepshead Bay this Saturday, where the annual Grillin’ On The Bay competition offers a panoply of gluttony. The grill-off, which costs $75-125 to enter and has delicacies for sale individually, features four categories: chicken, beef, pork ribs, and the enigmatic “chef’s choice.” If that’s not enough food, they’re also hosting the Brooklyn Chili Smack Down, a “people’s choice chili contest,” which is free to enter and just $10 for all-you-can-eat chili. To wash it all down, beer and nonalcoholic beverages will also be available for purchase.