I'm all for EDM, but not the EDM that was presented on ARTPOP. It didn't really go anywhere and it wasn't progressive at all. It is light years behind Skill, and any other EDM DJ who has put out music in 2013. What's even more embarrassing is that Gaga defended her knowledge of EDM and didn't even put any on her album

Aura comes closest, but uh, that's another story.
Glam rock, pop rock, with real instruments suits her well too. That's one direction she could venture into. It's pretty much her territory.
As for urban music, sure. Reloaded, Kandy Life, Starstruck, and Paper Gangsta are excellent. She could go for RnB with Do What U Want and Second Time Around like tracks. I'm here for it but she'll probably ruin it with stupid like lyrics about absolutely nothing.