Right now, the only known way to create gravity is with mass. To create Earth-like gravity, you would need a ball of mass as large as the Earth. The Earth doesn’t have the highest possible density, a neutron star or even a small black hole could create Earth-like gravity using a sphere of mass that is much smaller in diameter. Using the density of a neutron star, the sphere could be as small as 0.05 cubic kilometers. There is no way to create a black hole or a neutron star, that we know of. Black holes that small would be highly radioactive and evaporate very quickly. Neutron stars that small would explode. The smallest stable neutron star is about 20km in diameter and would have more gravity than our Sun. You may be able to do a base around a small blackhole that you discovered but the difficulty and cost, assuming it’s even possible, would make it not worth it. A spacecraft is absurd, there isn’t enough propellant in the entire star system to move something that heavy into a new orbit.
Scientists recently proved the existence of the Higgs Boson, the sub-atomic particle that gives other particles their mass. To imitate the majority of science fiction universes, you would need to be able to create artificial gravity without making your ship so massive that it’s impossible to move and you would need a way to create gravity in only one direction. Most world-builders use that concept because it’s the most practical for set design not because it’s scientifically plausible. Theoretical physics is still in the process of unifying the theory of gravity and quantum mechanics, which explains electromagnetism, the strong and weak forces. It’s possible that there is a connection between gravity and the other three forces, that would allow for some technology to create gravity without mass. The current candidates for the Theory of Everything do not predict such a possibility, but they are incomplete and do not accurately describe reality as we observe it. If there is some mechanism a technology could take advantage of, it would have to be something we wouldn’t have stumbled upon by accident. Even if we did discover such a mechanism, it would probably create gravity in all directions. Using negative energy, you may be able to warp space-time to make artificial gravity not effect all directions. Both are pipe dreams.
In my universe, the space stations spin to create artificial gravity, which is known as the centrifugal force. If the ring is large enough, the curvature of the floor isn’t a problem. Another issue is with the human biology. There is the Coriolis effect, which can cause nausea, loss of balance and inner ear problems. It is generally accepted a ring spinning at 0-2 RPM requires little to no adaptation, 2-4 RPM requires some training, 4-6 RPM requires extensive training and 6-10 RPM should be limited to military use only. The amount of artificial gravity is based on the equation: F=m(v^2/r) so you can increase the radius or increase the revolutions per minute. To create a spinning ring with Earth-like gravity at a slow enough RPM to prevent discomfort to the average person, the ring needs to be fairly large, larger than anything our current rockets could put into orbit in one go.
In the picture above, you can see how the floor curves up on the horizon. It has two rings with a radius of 2.8 kilometers, spinning in opposite directions and orbits the Sun between Earth and Venus. One side is always facing the Sun and converts solar energy into electricity. There is two rings spinning in opposite directions to cancel each other out, so it doesn’t tumble as it spins to keep it’s solar panels facing the Sun as it orbits. There is also enough room to grow enough food in hydroponic farms to support the population. To be honest, by the time we build such a space station, our farming area per person would probably be lower, since we will have more efficient farming due to genetic engineering. The following is a spreadsheet I created for calculating the specifications of space stations.