Can’t wait until Jan. 16 to see the new and (perhaps) improved “American Idol’’? You don’t have to. In a bid to generate a little buzz about the show, whose ratings faltered slightly last season, the friendly folks at Fox are giving fans in 11 US cities an opportunity to watch the Season 12 premiere a week before it airs. In Boston, the network is airing the first “Idol’’ episode Wednesday at the AMC Boston Common, and afterward host Ryan Seacrest and judges Mariah Carey, Randy Jackson, Nicki Minaj, and Keith Urban will take part in a Q&A that will be uplinked via satellite (and live streamed.) Want to go? RSVP at www.idolrsvp.com. But it’s first-come first-served so get there early.