Arkham City is no doubt the best and most complete Superhero game of all time, it was probably the best game of 2011(Skyrim fans might disagree) and it left a lot of doors wide open for a sequel, until then we will have the chance to play a new dlc: Harley's Revenge, a story driven expansion to an already wonderful game, but it's not likely this will influence the outcome of a sequel too much.
What would the game be called?
I have 3 options here: the first would be Batman - Gotham City, after Arkham Asylum was shut down they moved all the inmates to Arkham city and the logical explanation would be to expand the open world even more in Gotham and probably Bludhaven as it was mentioned countless times in the game. The second name will more likely have to do with the secret room, in Arkham Asylum there was a secret room in the warden's office with plans for Arkham City, in Arkham City we had Scarecrow's boat with the secret entrance and the password use to open it could make for a good title : Gotham - City of Terror. The 3rd and last name has to do with Azrael saying that Batman has opened the gates of hell and from "(Batman)The Ashes of Arkham" a much bigger threat will emerge, this name is very likely because developers should want to keep both "Batman" and "Arkham" in all their batgames to keep a sense of continuity.
New faces that we expect to see?
After 2 great games, and even seeing Bruce Wayne in action at the begining of the second, Rocksteady owes it to the fans to bring Alfred into the game, even if it's only at the begining, also after seeing Gordon in both games
his daughter would deserve at least a cameo for all her trouble. Justice League members could make cameos or be referenced.
How would events go down?
Arkahm Asylum gave us a pretty big sandbox to play around with, Arkham City gave us even more, so it is most likely that we will have a massive Open World , Rocksteady might make the city a little smaller due to attacks or earthquakes so that players won't have to deal with a GTA 4 size city, this will make the need of the Batmobile or Batpod more likely, but fans shouldn't expect the games' story or free roam to go for more than one day, this was RSs recipe of a good narrative and it's most likely they will keep it at a 8-10 hours story and reintroduce the side missions and riddles so that players could spend days in the game but it will still be the same night.
New villains that will make appearances:
Scarecrow is a candidate for the main villain after, the letter in the boat makes it clear he wants to make Gotham a city of terror with his fear toxin and we now he's alive after seeing his mask in Arkham City.
Killer Croc will most likely appear after his cameo in Arkham City
Red Hood - When playing the Joker's Carnival Challenge map with Robin, you can hear Joker say : "Robin? didn't I kill you already? oh well..." this makes an appearance from Jason Todd very likely.
Hush - we saw him leave Arkham City looking just like Bruce Wayne, so
Deathstroke - he was only present in Arkham City Lockdown for mobile phones, but as a fan favourite he would have his place in the game.
Who could return from the Arkham City villains?
Joker is not likely to return unless the devs find a really good way to reintroduce him,
Hugo Strange - well he is clearly dead, but he didn't go down without making Batman's life hard, Protocol 11 will no doubt serve a purpose in the sequel.
Mr. Freeze is grateful for Batman's help but could still appear, both as a villain and an ally.
Penguin, Two-Face, Poison Ivy,Bane(probably as a main villain after the most likely succes of The Dark Knight Rises), Calendar Man, Black Mask (cameo and challenge map appearance), Harley Quinn, Ra's al Ghul, Mad Hatter, Riddler all have reasons to return and have their shot against the Bat.
Playable Characters?(with improved combat and new gadgets)
Batman - no mistery here
Catwoman - it was fun playing as her in Arkham City, it's very possible she could make a return, even if only for Challenge Maps.
Robin - players will finally play with him (except Riddler's Challenges of course) in the Harley Quinn dlc, and he could get more that a cameo in the next game.
Nightwing - as I mentioned earlier, Bludhaven is a possibility, so that could give Dick Grayson a purpose in a sequel.
Azrael? - this is also a good a guess as any, he followed Batman all over Arkham City, he is a match for Batman in a every way and could be a great addition to the franchise. More Characters could also finally make multiplayer a possibility.
The theme and atmosphere of the game:
While gliding trough Arkham City you could hear inmates saying al sorts of interesting things, for example "Arkham Asylum, Arkham City, what's next? all-out war in Gotham? maybe it's just a small hint, but when Azrael says that Batman has opened the Gates of Hell, it could be taken literally, because there is no other place to hold all the super villains, and this will mean chaos to Gotham City.
These are my toughts on what to expect from a 3rd installment of Rocksteady Studios star franchise, an expanded gaming experience with a great story, a wonderful incarnation of the popular superhero and countless hours of gameplay after the main story is completed.