I have a new theory on Joker's past/present. What if Gordon was accidentally responsible for the creation of Joker? Gordon says that the felon is known for a couple of arm robberies, well either Joker is still Jack Napier or whatever his name is and is still pulling small-time heists or he's either already turned into Joker and is already leaving his calling card at the scene of his victims' dead bodies.
If this is the case than Joker would've been created before Bruce Wayne/Batman ever arrived back to Gotham, thus could become the explanation why Gordon is busted down to being a measley Lt. and working with Flass who he really doesn't have any business working with in the first place because Flass is a bum and a crook.
Like what if Gordon had the chance to save Joker ala Batman in "Batman 89'" at the chemical plant, but Joker slipped out of Gordon's hand and fell into the vat never to be seen or heard of again. Loeb could easily take this incident and bust Gordon down so fast it would make his head spin, thus explaining why Gordon is Lt. in "Batman Begins."
As for a hideout Joker escapes to I'll say a worned down apartment like in "BTAS" where he'll make his prop-gags, set up his team of clown henchmen, and mingle with Harley.