For a rather straight forward setup a camcorder or DSLR with 3.5mm jack for external mic would be the simplest to operate. There are affordable plug-in power mics made for video setups like this. It will need either a tripod or another person to hold the camera. This would be good quality video, and decent audio. No sync needed in post. However, the audio may leave you wanting more, specially for a music application.
Example of an on camera mic:
https://www.rode.com/microphones/stereovideomicprocWireless audio is an animal in itself, I would suggest exhausting all wired options before considering wireless mics. This is especially true for equipment rated for consumer use. Consumer wireless audio (gear that does not require licensing for frequencies) has to share the air waves with all the other wireless devices out there.
Separating the camera and microphone usually produces better results in music recording. If you want to do that without wires, it is probably better to consider a two device solution before thinking about wireless mics. A portable recorder like a Zoom, Roland, Tascam, Sony, etc., plus camera. Syncing audio in post is easy, and doesn't have to cost anything if you prepare the recording session well. All you need is a clapper, or just use hands to clap. What you do is record audio on both devices, camera and recorder, then film yourself clapping for every single take. In post, you just line up the spikes in the wav to the point of contact in the clap.
If you are a DIY person, this may give you some ideas. It is just one example, search around:
https://www.theblackandblue.com/2011/07/21/diy-film-slate/Choose a GoPro if you want to use it as a POV camera. For example, strapping it to your head, your body, somewhere on the piano that is impractical to place more conventional cameras. It is also good for placing in a highly visible area that needs a low profile. If you do not intend to use a GoPro like this, then you really have to think hard why you want to get one. You will be paying a premium for a camera that excels in certain scenarios, yet not using the camera in those said scenarios.
An example of the perspective an action cam can give:
A camcorder or DSLR, would offer far more flexibility in focal range than an action camera like a GoPro. Not to mention they will likely have larger imaging sensors, which generally equates to better video quality. If you want to save some money, you could go search for a used DSLR and some nice lenses. You mentioned you are looking for quality, and that is part of the reason I am suggesting the DSLR route.
Also think about how you will review your footage on site. A camcorder or DSLR have typically have a decent sized screen. What about the GoPro? Or will you be lugging a tablet or laptop around with you to pop the memory card in to review the footage.
As for microphones, to echo indianajo, please don't use SM58 or SM57 to record piano. Just don't. These mics are everywhere, they are good at recording some things, it's just piano is not one of them IMO. There are portable recorders that offer phantom power, so going with better mics than the built in ones is still an option. It is a balance between isolation and ambient. Considering you want to do a street recording, I would think some ambient is acceptable to establish context. Close micing will bring more isolation, but doing that on pianos has the potential for hot spots or a boxy sound. Ambient mic recording could work if the surrounding noise levels are reasonable. You might want to search around for mics designed for field recording.
Also checkout this thread I made recently. There are some examples of portable recorders here.
https://www.pianostreet.com/smf/index.php?topic=63279.0To summarize:
All-in-one camera. Easy to operate, not optimal quality.
Camera and portable recorder. Allows independent positioning.
Camera, portable recorder with mic preamps, discrete microphones. Potential for the best sound out of these options, more gear to deal with when working in the field.