To understand the uses of artificial gravity, you can look at things like magnetism and, well, real gravity.
Magnetism helps keep your kids' drawings on the fridge, but it's also what powers railguns. Where magnets fail is that they only work on some materials, so your forces could fill in those gaps. Magnetism is also part of the same forces behind electricity, so it's possible your forces could be used in electronics.
As for gravity, it's great for bringing things together. If you want to go somewhere, and it's got gravitational forces pulling you there, it should be easier for you to get there. Similarly, if you're trying to get away from something, gravity might keep you from being able to do that easily.
Aside from mimicking or replacing these forces, your artificial gravity could also oppose them. For instance, electromagnetic shielding or antigragivty.
All of this really depends on the power and cost of your artificial gravity generators. If they're strong and cheap, they can probably be used for a lot of things. If not, people will probably just stick with magnets. The really interesting part would be if this technology is so massive that it creates free energy. Because then you could make perpetual motion machines, and do all kinds of impossible stuff. But like I said, it depends. Plug in your idea of how powerful this technology is, and see what you come up with.