Do I really need a well?
You can purchase a Well that allows you to fill up your watering can, but I find myself with patches of water on my farm and rivers flowing all around me.
Is there ever an instance where this water will not be available and a well would help me, or would I just be buying this for the convenience of placing a water source where I want it?
You don't need a well. You can always fill your watering can up at the ponds on your farm, but depending on how your crops are spread out a well placed well can save you a lot of time.