I would think that dissolving a non-reactive salt, like $\ce{NaCl}$ in water can be considered as a physical change. This is because, you can recover the salt by evaporating the water away.
From the Wikipedia page of physical change
In general a physical change is reversible using physical means. For example, salt dissolved in water can be recovered by allowing the water to evaporate.
But the distinction between physical and chemical change can be misleading and confusing at times. In general, anything that does not change the chemical constitution of the substance, is a physical change.
When you dissolve $\ce{NH3}$ in water, the following equilibrium is set up:
$$\ce{NH3 + H2O <=> NH4+ + OH-}$$
But if you heat the water up, you will get back the original ammonia without any chemical change in its composition. However, the ammonia does change its chemical composition in water, as $\ce{NH4+}$ ions are formed. By that argument, you can say that the dissolution of an ionizable salt is a chemical change.
In some cases, dissolution of a compound can be called a true chemical reaction. For example, when you dissolve Calcium oxide ($\ce{CaO}$) in water, a vigorous chemical reaction takes place, forming $\ce{Ca(OH)2}$. You cannot get back the original $\ce{CaO}$ by just evaporating the water. In case of aqueous solution of $\ce{AlCl3}$, if you try to evaporate the water by heating the solution, you will get back only $\ce{Al(OH)3}$ as anhydrous $\ce{AlCl3}$ reacts with water as soon as it is in contact with water, to form $\ce{Al[H2O]6Cl3}$.
What I am trying to say is that some changes can be classified into one of these types, while some other changes can not be given a clear classification. Melting of water is clearly a physical change, while reaction of $\ce{H2}$ and $\ce{O2}$ is clearly a chemical change. One another fact, putting paint on a canvas is not always a physical change. In fact some paints are manufactured in such a way that during drying, some chemical reactions occur, due to which the paint fixes firmly on the surface. This is the reason many water thinnable paints can not be dissolved in water once they become dry.
To conclude, you should not hold hard classifications like that in your mind. However, my final verdict: Dissolving a salt is physical change (mostly).