They make sound insulating and deadening foam. Put the piano in a small internal room and line the room with acoustic foam: http://amzn.to/1o9CGjb Living closer to work must be worth 2 of these for $160?
This sort of foam isn't for soundproofing, but for reflection-proofing. If you treat your room with this and make noise, your neighbors will still hear it just as loudly as before, but inside your own room, the sound will have less reverberation and echoes, making it sound more focused.
For soundproofing you need dense materials with lots of mass. Things like mass loaded vinyl, rockwool sheets, or even full-on room in a room. It can get pretty expensive [0]
I agree with the other commentor, a nice digital piano with headphones, or speakers you can adjust the volume out of would be the best option.
Yeah, foam doesn't really "soundproof" anything. Foam is normally for sound treatment, so you get less interference when making music for mixing / mastering / recording purposes. You need extra drywall / more insulation / sheetrock / mass loaded vinyl / wall decoupling to actually block sound.
I actually have an electric piano as well and even though it has a mechanical action but it still doesn't come close unfortunately.
I guess I am relatively serious for an amateur but the piano is a very difficult instrument to master and so I just feel like since I have such a limited time to practice I rather make that time as effective as possible. That means playing on an acoustic and thus making a lot of noise sadly..
The "make it sound like a wood-and-felt-and-wire piano" issue is solved. The "make the key action feel like a physical piano" is (based on my extensive side-by-side testing) close enough to solved that -if one's concerned about bothering the neighbors with the sound of your playing and one has the money- purchasing a good model is a no-brainer.
I actually had one of these and can tell you that unfortunately the technology just isn't there.
The action is the same but the way it reacts and sounds isn't, and at least for classical music, learning the nuances of the sound (and pedal!) is the hardest part..
There are two broad categories of approaches you use when dealing with sound. One is controlling sound transmission, and the other is shaping/controlling diffusion. In general these types of foams act as diffusers, which influences the sound inside the room, but have very little impact on sound transmission, which is what most people think of when they say 'sound proofing'. Dealing with sound transmission generally requires lots of mass, isolation, and careful attention of air-tightness. Think about how a thermos is constructed and you start to get the idea.