I need copper for crafting. I've found it in some random caves, but usually only find about one copper per location. Are there specific maps/missions that have more caves and are more reliable for finding copper? Is copper available inside other items or by other methods?
Copper can be found in any "cave-like" area where rocks could be on the walls or ceiling. This includes mines, actual caves, and even sometimes just "quarries". Copper ore has a chance of replacing any of these rocks. The same goes for Quartz, Rough Ore, and Coal.
Caves are most common in forest zones (compared to suburbs, city, and industrial zones) since they have a chance of appearing in the main center area. However, every map type usually has a few caves on the outside edges of the map (which are forest-based).
Occasionally, copper ore will be given as a reward for completing a mission. Be sure to check the mission rewards ahead of time so you know what you're getting. Accomplishing bonus objectives (staying under the build limit, finishing the mission within the speed run time limit, etc) will earn you more resources in the form of higher level loot chests.
Finally, encampments occasionally give a copper ore as a rewards as well. You can tell what kind of rewards an encampment will give by hovering your reticle over the encampment when you're close. If the reward symbol is a piece of copper ore, you will receive 4 pieces of ore.
All of the info above also applies to silver ore (the tier 2 ore) and malachite (the tier 3 ore).
From my own experience playing, copper was most common in natural areas, specifically caves and mine shafts and not in industrial or suburban areas.
Other places to obtain copper include chests/lootable items in the world and as rewards for missions occasionally (it's a random chance and you can see the rewards before starting a mission).
I have found an abundance of copper in boxes within a cave system. So if there is copper in the cave, then the boxes you can loot (excluding the ammo boxes) seem to have an increased chance of providing copper. In addition, any weapons that you get from looting can produce copper (or silver etc) in the recycling process. The higher power level you are, the better chance you have of getting plenty as you farm. Work on increasing your power level (which is NOT necessarily in relation to your quest progression line!!! Check out your survivor squads, paying close attention to the directions for each squad slot. Changing the lead/survivors and upgrading them can increase your power level by 2-5 in a couple minutes.
As your power level increases, the map opens and allows you to access higher level missions. The higher the level, the more likely you are to find more resources you need. Finally, search with a "Jess" hero if possible. She is the best for looting, and will often increase the loot..and has the added benefit of making it easier to farm.
Try joining some friends for a couple specific farming missions.. you'll get quite a bit.
The best suggestion.. SEARCH EVERYTHING THAT CAN BE SEARCHED!!!! Specifically any boxes, piles of rubbish, bins, survivor shacks, and barrels.