This is a very interesting question and extremely important. But it is an open question with no answer. There are lots of people thinking about this and trying experiments to get a hold on this. Probably the most interesting experiments along these lines are the cooling of micro-cantilevers: they are trying to make very small mechanical oscillators (like tiny diving boards) and then cool them to the ground state, allowing observation of quantum effects on a macroscopic (well microscopic, but big compared to an atom) object. So far, this has not been done, but in a year or two, it probably will have been done.
But the difference between quantum physics and classical physics is not size, as many people seem to think. It is energy. There are macroscopic devices that do behave quantum mechanically. For example, current carrying loops with Josephson Junctions have been made that display quantum mechanical currents, even though the device is big enough to be seen by eye. But, to see these currents, you need to strip all the energy out of the system. As soon as there is too much energy, the quantum behavior can not be seen above the classical noise.
Going to low energy is not a trivial concept because energy in any physical system is spread among a large number of degrees of freedom. You can cool one degree down to low energy and see quantum behavior, but only if you can isolate it from the other degrees of freedom. The easier the system shares energy between degrees of freedom, the harder this becomes. I guess this is a long winded way of saying the size scale (or more accurately, the energy scale) at which a system switches from classical to quantum depends entirely on the system. And can range over many many orders of magnitude. Probably the best way to define a scale is to find the typical energy quanta for a given system and multiply by a factor of 10 to 100. That should roughly give the point (in energy) for that system where it begins to lose its quantum behavior.
It really doesn't have anything to do with the uncertainty principle, since the uncertainty principle has very little to do with a lot of quantum physics. In fat, the uncertainty principle has more to do with how well you know (or can know) the system than it does with the quantum behavior of the system.
There is an interesting idea that Roger Penrose proposed on the classical/quantum scale and why large things do not behave quantum mechanically. It has to do with the incompatibility of quantum mechanics and general relativity. Imagine you have a massive object. And you put it in a superposition, so that the two states of the superposition have different locations in space. Well, relativity tells us that a massive particle in space will bend space-time. So not only do you have a superposition of two locations of your particle, but you have a superposition of two space-times corresponding to those two locations of the particle. General relativity also tells us that there can only be one space-time, so having two of them is impossible. However, there is a similar relation to the Heisnberg uncertainty principle: there is an energy-time uncertainty relation. This tells us the bigger the uncertainty in energy, the smaller the uncertainty is in time.
Let's assume there were two space times for now, regardless of what relativity says. The difference between the two space-times, leads to a difference in gravitational energy of the two states (kind of like a self gravitational energy).
Now, we know that there can not be two space-times, so there can't be this difference in energy. In other words, the difference in energy must be zero. Therefore, the UNCERTAINTY in energy for our superposition must be equal to the difference in energy of the two states, so that our superposition is still consistent with relativity. This means there must be a time in which such a superposition collapses given by the time-energy uncertainty. The larger that energy difference, the faster the time. Therefore, the more massive your particle is (or the farther spacially separated the two superposition states), the faster a quantum superposition of such a particle must decohere or collapse. This puts a time limit on how long a massive object can behave quantum mechanically. And, for anything more than a few hundred atoms, this time is very very short. Of course, this is just a theory.