First let me say right up front that growing an upside down tomato is not for everyone. Hanging, with damp soil, an upside down tomato bucket can easily weigh 50 pounds. I have mine hung on shepherds’ hooks – I put two together to add to stability, and still, as soon as I hung up one upside down tomato, the pole started to bend, even with just a tiny seedling. I then tied both hooks to a piece of rebar, sunk feet into the ground for reinforcement.
There are a few other ways to hang upside down tomatoes. I have seen upside down tomato buckets hanging from square structures made of 4X4 beams - think hockey goal without the net - which is a good solution if you have a place in your yard for that, and can sink the 4X4s deeply into the ground.
If you have a wall in a full sun area, you can get a hook and attach it to your house, or porch, but make sure the hook and screws are tough enough to hold the weight of your upside down tomato.
Tomatoes are sun lovers and need at least 6 plus hours per day, so be sure, wherever you hang your upside down tomato, it really gets full sun. It’s easy and very common to overestimate how much sun an area gets. Don’t just assume or guess about an area you’re considering. Make sure you’ve got enough sun, by either visually timing how long the sun is hitting the area using a watch (no cheating), or use a sun calculator.
The variety particularly important if you are growing an upside down tomato. My advice is to stick with a cherry tomato, because some of the bigger fruited tomatoes are too heavy when ripe, and the weight of the fruit can break the upside down tomato plant.