There are several places you can mine runite ore now, if you are a free player there are only two runite rocks avaliable to you, located above the lava maze in level 46 wilderness. If using this spot watch out for revenants!
Members have seven more rocks that they can access, they are as follows: 2 located in the Heroes' Guild basement by the fountain of heroes. One in the dungeon underneath the Lava Maze which is guarded by level 64 poison spiders and 2 black dragons One is surrounded by several dangerous Dark Beasts under West Ardougne on the way to the Temple of Light as featured in the Mourning's Ends Part II quest. One in the centre of the Fremennik Isles (reward for The Fremennik Isles quest), north-east of Neitiznot. Two more are accessible in the North Keldagrim mining area accessible after the completion of the Forgiveness of a Chaos Dwarf quest.
Keep in mind that runite rocks take a long time to respawn (anywhere between 12 and 25 minutes depending on how many people online), you may wish to server hop to make the most of your time and get as much runite as possible.