A person who came close enough to the Sun to get some in the nose would be unable to process any sensation other than instant combustion, and so the Sun cannot be said to smell like anything. Smell is not an intrinsic property of matter the way mass is. Instead, it's a wholly subjective result of molecules coming into contact with the olfactory cilia inside the nose.
Molecules picked up by these cilia trigger a series of nerve impulses to the brain, which then processes the data and checks it against memories of other scents to properly identify it. None of the organic tissues of the human body could withstand the slightest contact with the highly energetic plasma ejected from a star. This makes the subjective experience of aroma detection impossible to accomplish before the nearly instant incineration would render the question moot.
Even if the temperature of the Sun could be brought down to tolerable levels, there is still no good way to smell it. The matter in the Sun is almost entirely plasma. In this state, gas is stripped of its electrons, which leaves positively charged hydrogen nuclei sheathed in free-moving electron clouds. Because of this, the normal interaction between the negatively charged surfaces of scent particles and scent receptors becomes essentially impossible. The Sun, therefore, cannot be said to have an odor.