When my son moved into his first apartment, my gift to him was a box full of things he would need, but not necessarily think of getting. Simple things like napkins, paper towels, dish and laundry detergent, scouring pads, pot holders - all the little things you need - is a great help. Not only does it save the person a little money, but helps them get their new life off to a good start.
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When my brother graduated from college and got his first apartment, I tried to think of something that he could really use, and wouldn't get for himself.
I needed a housewarming present for my cousin's daughters and I didn't have any money. But I do have a lot of plants, so I've started taking cuttings and rooting them in water for about two months now.