As mentioned, tools, which can get very pricey, especially if you are starting from scratch (basic screwdrivers, etc.).
Also, every time we move (which is fairly often), there are little things. An extra trash can. An entry mat. A new area rug because the old one doesn't fit in a smaller space. Getting a spare key made. A closet dowel and hanging pieces because you need an extra bar in the tiny closet. New toilet brushes. Whatever. Just lots of little things, some of which are fairly necessary and others of which are just really nice to have.
And if you are someone who likes to have you home Just So, then hundreds or probably thousands on the right floor lap to go in a specific space and a vase the right shape to go in that nook and wall hangings of some kind to go on that long wall in the entry, and... These are the ones that can fairly easily be kept in check, but that you have to watch carefully if so included. They are also the ones that you can actually budget for. If you've spent your numbers, you don't buy. But again, you have to have that number set ahead of time and track that you don't overspend.
Also, I can't recommend enough seeing if you new neighborhood has a Buy Nothing group on Facebook. In mine, the most generous things are given away almost daily and it is ideal for someone moving.