I like the Riddler and Lex as the main villains. The Riddler teams up with Lex(unbeknownst to anybody) who promises him a grand showing of his game. An alien with super powers has just revealed himself to the world, I bet the Riddler would just love to put both he and Batman through a game. Have him be like Gerard Butler's character from Law Abiding Citizen.
It would go something like this: The Riddler shows up in Metropolis and starts putting people in traps. They die. And Lex tasks Superman with finding The Riddler. He ends up finding him and having him thrown in jail. The Riddler tells him that it's not over and that he's kidnapped a bunch of school girls and they will blow up if he doesn't solve the riddle. Superman doesn't want to play and tries to use his powers to find the missing girls, but to no avail. He then decides to try and solve the riddle.
The riddle stomps Superman, who then seeks outside help and some background info on The Riddler. He travels to Gotham where he meets Batman. I guess this is where they can have their little fight, but to me them fighting doesn't really fit in this scenario.
He ask Batman for help with the riddle and they both work together to solve it. [It's not as simple as this, but I wanted to shorten things out.] It turns out that this is exactly what the Riddler wanted, and they are only playing into his game. He wanted to be caught, he wanted Superman to find Batman and for them to work together.
As this is going on, there is a presidential election going on between the incumbent and Lex Luthor. In a debate, the incumbent expresses that he's against Superman and vigilantes, Lex expresses that he supports them, and will do everything in his power to help Superman and Batman save the girls.
Batman and Superman save the girls and beat the Riddler. Months pass by, Batman is back in Gotham doing his thing, Lex wins the election on the back of Superman(he supported Superman and Batman throughout the whole thing and made it known to the public). Then Batman discovers that there was a connection between Lex and the Riddler. He travels back to Metropolis to tell Superman, and Superman confronts President Luthor about it all. He initially denies it, but Superman presents him with the evidence, and like a switch was flipped, the good guy we seen throughout the movie all of a sudden turns psychopath. Flashbacks show that he hired the Riddler, and then reveals that he did it all to win the election and then he expresses his utter disgust about everything that is Superman.
It's revealed that Lex created an army of droids out of Zod's armor, and in the scenario that Superman turns against them, the program would be activated. Lex activates the program and the final battle between Superman and the droids begins. Superman wins, but Lex is still the president. Batman leaks all the documents about Lex and the Riddler online for the world to know. Nothing can be done about it because the evidence isn't enough proof to impeach, but it's enough to make people wary of Lex, and also draw them closer to Superman.
At the end of the movie, Batman and Superman meet up in a very Batman Begins ending type of way, they talk. Batman ask Superman, "what about Lex"? Superman responds "I'll deal with it". Superman hears a crime going down in the world somewhere and turns his head, he's about to leave when he turns back to say something else to Batman, but Batman is gone. Superman smiles, and the movie ends with him flying off.
For the tl;dr crowd.
Riddler comes to metropolis and sets up a game for Superman. He kidnaps a group of girls.
Superman teams up with Batman to solve the riddles
Lex is running for president and publicly supports Superman and Batman, the incumbent does not
Superman and Batman solve the riddles and save the girls, Lex wins the election due in large part to his support of Superman/Batman
It's eventually revealed that Lex hired the Riddler, his endgame being the presidency
Superman confronts Lex, truth revealed, Superman battles an army of droids created using metal from Zod's armor and attacks based on the world engine
Lex remains president because not enough evidence