I don't think there is any. However, teleports can help you get nearer. For example, from any gold mine you can use a teleport to Falador or to Varrock to get near a bank. To get back to the gold mine, it depends which gold mine; for the one at the Crafting Guild, use the Explorer Ring (this requires doing the Lumbridge/Draynor achievement diaries).
best Place To Cut Willows Is By Draynor Bank.
The mines near Seers, it's a coal mine and there are trucks nearby that can hold up to 400 coal, after the cart is full, go back to seers and there's a cart station just near bank, take out your coal and bank it, simple, rinse and repeat.
Depends what you are cutting. If you are cutting normal trees, around the Grand Exchange would be the best place. If you're cutting oak trees, northwest of the northern varrok bank would be the best. If you're cutting willow north of the draynor bank would be the best. If you're cutting yews south of falador would be the best. If you're cutting member logs look it up on runescape wiki.
The Wilderness.
The best way to fish on runescape is to use a net or a fishing rod and bait in draynor. Then it is easy to bank your fish
Fishing guide
There are many cooking ranges on runescape. The best cooking range on runescape is at Al-Kharid. It is the closest to a bank.
The best place to kill zombies is at the armor zombie place. IT is where everyone get 99 str.
Lumbridge North, McGrubor's Woods North, Yanille, Entrana - Out of all those the best place is Yanille, It being the closest to a bank, plus fast access for P.O.H owners.
Living Rock Caverns
stronghold of secutity i like
grand exchange.