Radio controlled watches also keep time independently from the atomic clock since they are also quartz movements. The grade of quartz is often lower in these watches since it doesn't need to be as accurate as regular movements, but even those watches should be in the realm of 0.1 sec a day. That's accurate enough for most people.
The most accurate quartz watches are temperature compensated & certified as chronometers. Such watches may keep time within 10 seconds a year or even less.
From experience I would recommend avoiding solar powered watches like Eco-drive models, since even those will require replacement capacitors. They may run up to 10 years but eventually wont hold a charge. A certified watchmaker will often charge easily 5-10 times the price of a normal battery replacement for replacing the capacitor in a solar powered watch & often small independent watchmakers aren't able to get the parts. On the other hand normal battery changes can be performed even by a novice at home with the right tools.
Depending on what you are willing to spend, there are many solid affordable (as well as high-end) offerings from Citizen, Casio & Seiko that will keep excellent time. From there you may look into ETA quartz movements, as those are very well engineered & fully serviceable (which many Japanese movements are not) with parts readily available to every watchmaker.
But even the Japanese movements will often last you decades.
Being a watchmaker myself I am predictably biased towards analoge watches, since models with digital electronic displays are largely unserviceable (often the case cant even be opened), but they wont keep any worse time. Due to the power requirements of those LCDs however, as well as many extra functions & back lighting often packed into those watches, the battery usually wont last as long as on analoge models.