I tend to hop back and forth between metropolis and Gotham doing missions. Also the welcome to watchtower mission is worth alot of exp. I leveled up mostly from that one mission, from 9-10. Make sure to pick up the other missions in the area where your mentor sends you. You will end up doing like 2-3 missions in one spot. I also do the wanted missions. They are worth alot as well, like 2300+ experience. if you are on pvp server get the "defeat 5 villian players" mission. It's repeatable and you finish it just by fighting another player when you can. You can do it on pve but you have to toggle your pvp and so does your opponent. On pvp server just doing missions I usually have to kill one Ayer who attacks me. Or if you do the legends it will count from that match as well. You get it from midtown police station. It's outside on the wall.
