Quantum mechanics threshold
Newtonian physics is generally a good approximation in a problem as long as any significant differences in the action involved in the problem are much larger than Planck's constant (if not, quantum mechanics will be needed), the speeds involved in the problem are much less than the speed of light (if not, special relativity will be needed), and as long as the Schwarzschild radius of any gravitating object in the problem is much smaller than the object's radius (if not, general relativity will be needed). In addition, if a problem meets the criteria for needing both quantum mechanics and special relativity, then quantum field theory is needed.
Quantum mechanics is generally adequate for analyzing the electrons within atoms, but quantum field theory is generally needed for any other kind of subatomic particles.
The above are really just rules of thumb. For example, macroscopic quantum phenomena exist, in which quantum phenomena are apparent at a macroscopic scale.
The answer depends on the thermodynamic temperature of the environment of these objects, the interaction strength with which they couple to this environment and their lifetime.
The spatially largest and consequently longest lived observed quantum effects, that I am aware of, are interference fringes of light that came from galaxies that are millions of lightyears away. The reason why these photons didn't suffer from decoherence is because they are very long lived (photon lifetime is infinite in the theory) and the universe is both very cold and only thinly populated with atoms which could scatter these photons. As a result, the light that was emitted so long ago is still coherent and will show the exact same interference terms that one would expect from a light source just a few feet away in the laboratory.
No other thresholds comparable to quantum-classical are known, nor is there any reason known at present to suspect them.
The precise threshold between quantum and classical physics is actually rather simply: it is ignorance (quantum) vs knowledge (classical).
More precisely, regardless of the sizes or masses or scales involved, quantum rules always apply when there is absolutely no trace of information anywhere in the universe about what is happening. In such cases of true and absolute ignorance, the hidden entity will in a strange and probabilistic way attempt to explore every possible history left open to that is compatible with the laws of physics and the "envelope of ignorance" that the rest of the universe sees for the system.
The result of this exploration of all options available is called the integral of all possible histories, and it is the direct source of all the wavelike and probabilistic behavior that we find so odd in quantum mechanics. For example, a single particle begins to look like a wave because within its envelope of ignorance it is forced (it's not an option ) to explore an infinite number of smoothly similar and nearby paths.
In contrast, once any information leaves about what is going on leaves the system and irreversibly becomes part of the outside universe, that aspect of the entity ceases to follow quantum rules and becomes part of classical physics, which allows only one possible future to be explored at a time.
The main reason why no other quantum-classical thresholds seem likely is that the above rules are really just different aspects of the same phenomena. That is, information is by definition the loss of the quantum default of unbounded exploration of all open options, forcing some part of the universe to become specific, real, and historical. Without this deep and essentially tautological relationship between between quantum generality and classical specificity, concepts such as history and information would cease to have meaning. After all, a universe in which all things are happening at once is in the end no different from a universe in which nothing ever happened at all.