One of the most simple gift ideas that I so often forget? Plants!
I have a very enthusiastic aloe plant on my sunny kitchen window sill that has been split, re-potted, and shared many times as a farewell gift, housewarming, thank-you, etc. Houseplants have all kinds of benefits, and aloe is great to keep in the kitchen for burns. It benefits my plant too, which has a habit of growing too big for its pot.
You can go fancy, purchasing a new pot or painting a custom container for it, or more casual if the recipient is a bit of a green thumb and able to re-pot it themselves. It only took a short time for me to re-pot a piece for my roommate's darling girlfriend, and it even looks sufficiently festive with the bright green spikes and red bow!