You don't need lockpicks, just the skill. There is a skill book in Farglow in the training area, which I used to learn Lockpick (to open a hidden chest by one of the buildings), and I maxed it fairly early. Some people leave locked chests until later, and come back for them to get better quality loot (which tends to scale to your level), but later in the game gold isn't a problem and there are merchants to buy stuff from if random drops and quest rewards are not sufficient.
If you go through the miller's kitchen there is a large, hanging (IIRC) pot there with lettuce, etc, sticking out of it, with the key at the bottom (stand close and look down). It is just to the right of a counter with bread on it, etc.