My suggestion would be to use Bill Shatner as the villain (or one of them at any rate) in the next film.
With my fanboy hat on, I'd cast him as Emperor Tiberius from the Mirror Universe, a version of Kirk's briefly mentioned grandfather... with Pine, Quinto, Urban etc all playing their counterparts. The Terran Empire having studied their history and where the Defiant really came from, are planning a full scale invasion. They discover a rift which leads them to this new universe's Laurentian System... not where they originally planned to go, but once there they discover a Federation significantly weakened by Nero's actions.
My other request would be that they come from the same parallel dimension seen in ENT & TOS... that way the Abramsprise can go up against an Enterprise more closely based on the original. Some tweaks to the design, so that it holds up on the big screen but the same recognisable icon... in enemy hands.
*EDIT*
Actually scratch all that. It's too much and would completely lose the new audience. It takes away from the point of having a fresh start doesn't it? As a consquence, Bill has probably missed his chance... He turned down appearing on ENT Season 4, that was supposedly a significant role, which might've even saved the show from the axe for another year and therefore another guest shot in all probability. He then said he wasn't interested in doing a cameo for JJ Abrams. He should give up and accept that he passed up two golden opportunites already.
The next film should look at the 5 year mission of exploration and how such a young, inexperienced Captain could possibly be given a prestigious task like that. In this a whole new reality, they should perhaps steer clear of reimagining elements that were already perfect to begin with (MU, Khan, the Guardian, Tribbles) and instead create either new or improve poorly realised characters and situations that had potential. Take that kind of thing to a new level and it has no worries about falling short.