Big Cup, which some called the de facto Cheers for gay men in New York City, served its last cups of coffee on Sunday, after almost 11 years in business on Eighth Ave., another victim of rising rent. Big Cup held a special importance for young gay men who were new to the city and finding themselves. In recent years, a bunch of gay, lesbian, bisexual and transgender kids from local high schools would come in and hang out between classes. It was also a spot for the after-theater crowd, and even parents with strollers from the neighborhood were customers. The place was sort of a town square for Chelsea, albeit more so for gay male Chelsea.