While TDKR did leave it open for sequels to be made, going several different routes (I won't say, for fear of spoiling it for those who haven't seen it but you who have seen it will know what I mean), I'm pretty sure that the next movie won't follow on from it.
I imagine that they'll go down the Sony/ Spider-man route and reboot fairly swiftly, but I don't think that it will be another origin story like The Amazing Spider-man. I think that they'll take the James Bond route - have our hero as an established hero and assume that the audience knows how he got to be here. A sort of alternative sequel to Batman Begins, Superman Returns without the gap years or The Incredible Hulk.
Given how successful the Nolan movies were, I don't expect this to go down the Shumacher-route and mark a total contrast with the previous trilogy or even to be as different from it as TAS is from the Raimi movies. If I were a Warner exec, I'd want something in the same vein as Nolan's movies, but I'd obviously allow the new director and writer to move their own vision along. It's possible that it will be set up in a way as to meld with Snyder's Man of Steel but I don't get the impression that a common DC-verse is a big prioity for them.
But, as William Goldman said and as I like to quote - in Hollywood, no-one knows anything (least of all me). So expect the unanticipated.