If you want to bank, you have to go to East Falador. The Dwarven Mine is also a good spot for power mining, but the bank is not accessible to F2P players. Here, you can mine all 3 ores in one tick a piece by using a Rune Pickaxe, then drop all three, at this time the first rock you mined should respawn.This is known as “power mining.” However, it is often busy and low level players will have to deal with Scorpions(level 14) and bots. If you do not want/need the ores, then the best place are the 3 rocks in the Al Kharid Mine.
The fastest method of getting from level 15 to level 99 is by mining iron rocks.