For lower level miners, the mine north of Rimmington is a great starting point. It is free of the dangers of monsters and there are many low-level ore rocks. The two closest banks are roughly the same distance from the mine. One bank is in Draynor Village to the east, and the other bank is in Falador to the north. However, if you completed the quest Rocking Out, you can use the customs locker nearby for banking.