This question is out of scope, not in the simple sense of just this site. You need to realize that critical details that your question depends on are literally unknown at this point in history. That's because small black holes (which are easily implied by your question) involve quantum gravity - basically the area of physics where we know for a fact current theories don't work completely, and that there's new stuff to be discovered.
Also, as a matter of scope, it's not something we can do on the scale of society today. The reason is that small black holes are not naturally occurring. The only natural way we know of black holes forming are from collapse of stars, and only stars much larger than our sun. Obviously, that's not very small. Could "we" make small black holes? Yes, although the pronoun "we" is used extremely liberally here. Some advanced civilization could, this is almost certain. There is a size lower limit, which wasn't even known until people like Hawking. The black hole radiates faster and faster with lower mass. That means you need above a certain size to have it stable. Estimates I've seen range from the mass of Mt. Everest to the mass of the moon.
To address the "portable gravity device" I need to refer you to Gauss' law for gravity. This relates the mass within a volume to the gravitational flux over the surface. The gravitational flux is the gravity times the area. Gravity is a parameter we set due to the requirement that we create Earth gravity (which might be an absurd requirement by the time we're capable of making such a thing, for the record).
I imagine that you would use a rigid sphere with the black hole in the inside. The principle is then that you could stand on the outside of the sphere. Let's say that you're using the smallest stable black hole. Because of Gauss's law of gravity, the mass of the black hole needed is proportional to the area. This constant of mass divided by area is the same as for the Earth. But since surface area to volume ratio goes up with smaller size, you need higher density. This is the utility that black holes can provide. They are subatomic, and effectively points in space, allowing your structure to envelop any given density (provided you meet the stability requirement). With this setup, a black hole would allow you to create a sort of "micro-planet". You would have to have something to hold in the atmosphere still, but this could be tethered to the ground and wouldn't be particularly exotic.
So you have a sphere with a black hole in the middle tugging. That means the sphere has to have material strength to resist that tug. The requirement is almost identical to that of rotating artificial gravity habitats actually. It's the difference between the strength requirement for a spherical pressure vessel versus a tube, which is a factor of 2. Practically, this could be up to 1 km or so with fairly normal materials. It's a similar problem to building skyscrapers. Your surface has some load, which is your habitat, including people and all their things.
Is this a stable construction? No. Your structural sphere exerts no pull on the black hole because of the shell theorem. In reality, it's not perfectly symmetric, which means that the black hole will always be looking for some weak point in your mass distribution and will use that to eat your habitat. Naturally you would engineer around this, and it wouldn't even be particularly difficult. It could be done with gravitational "tugs" in the interior. Basically, large lead balls that you lower and raise according to how the black hole is moving. I should mention that this is only one of the several methods that are possible. Electromagnetic forces would be preferable. However, I know that some people caution about small black hole's values of angular momentum and charge values, because they might like to expel them quickly. But we can't say for sure. These is an open research area.
There is actually an extra proviso that can be used. The small black hole will emit radiation. Hopefully nice, roughly 5000 K radiation. You could reflect this off the inner walls. It would affect the growth/decay rate of the black hole, but who cares, its mass will budge very little for millions of years. That reflection would provide some lift to the surface, and it could even be used to eliminate the structural requirement. Basically, radiation could keep the surface afloat. The same principle has been noted for Dyson spheres. However, there are limited design variables. The upward pressure you can get from this is limited by the blackbody radiation law. That surface power rate is then limited by temperature. Temperature is what limits how small you can make the black hole.
So yes, this is all plausible. Whether it's practical is a different story. Even if everything goes perfectly you're still limited in the surface area to mass department. In short, if you tore apart Earth and made many micro-planets from it, you would end up with exactly the same surface area. That's not a very compelling business case. If we're so advanced that we can make black holes, then matter will probably have other uses, such as powering fusion power plants.
There is another hazard I have yet to mention of small sizes. Small size correlates with higher temperature, but in the strange world of quantum gravity, it can even make new particles at the temperature that roughly corresponds to the particle's rest mass. Photons can be made at any temperature - that's why we all give off thermal radiation. But at higher temperature, neutrinos, electrons, and others can be made. This isn't particularly very good news. If the black hole is too small, it will make an exotic zoo of particles that would make any modern particle physicist envious (it's also dangerous). It is just one more reason that small black holes present dangers. But thankfully we won't encounter them anytime soon.