Our family had a piano in a townhome for several years, and then I had an upright in a condo. The neighbors could hear me, but I always told them to let me know if there were certain times that were not good for practicing, and it was never a problem. I actually had problems with the fireman upstairs blasting music in the middle of the night-- took me over a year to realize that there were probably city noise ordinances (there were), which is when he finally stopped. My current neighbors love to hear me play :)
It's good that you wouldn't have someone directly under you, because the vibrations go right into the floor! A few tricks to dampen the sound are to stick towels into the back panels of an upright, or to put a rug under the piano. I also would do my best to avoid putting the piano against an adjoining wall. But also make sure that you don't put the piano against an outside wall, since the temperature fluctuations aren't good for the instrument.
If your piano is too loud for the space and the towel trick doesn't work, a good technician can also voice down the hammers for you (definitely find a trusted technician to do this, since it requires skill and is difficult to undo).