I'd like it if Riddler was kind of mysterious like the Joker but is more like america's most wanted, he's a con artist turned theif turned hacker, who is known by the FBI for moving through most of America and doing a string of Riddle Crimes. He's taken on the CIA, FBI, and many police departments even different mobs but Batman has caught his eye.
Either that or I'd have him as a sort of conspiracy theorist type character, who has theorised that Batman isn't the killer or doesn't believe it and is setting out to prove it using the evidence he has brought together as Riddles for people to find and its kind of race for Batman to catch Riddler before his riddles spill the beans about Dent.
I think the second idea is an interesting idea but to be honest I much prefer the first idea its closer to the riddler in my opinion and seems the most interesting, although if they mould the two together it would be cool.