Hybridization of sulfur in sulfur dioxide
The structure of sulfur dioxide ($\ce{SO2}$) is quite complicated.
The image from socratic.org* explains it quite well, please find the $\ce{SO2}$ hybridization diagram via the Internet Archive.
As seen, all the atoms have $\ce{sp^2}$ hybridization.
I'll only focus on the central sulfur atom.

Two $\ce{sp^2}$ orbitals form $\ce{\sigma}$-bonds with the two oxygens.
The other $\ce{sp^2}$ orbital is where the lone pair lives in.

Now, we have dealt with 4 electrons, and only have 2 electrons to deal with.
The 2 remaining electrons actually live in the unhybridized $\ce{p}$ orbital.
At this point, the two oxygen atoms will also have 2 electrons left to pair with the sulfur atom.

The two oxygen atoms get to keep their own electron.
Sulfur shares two electrons among itself and the other two oxygen atoms.

Thus, no electron lives in the $\ce{d}$ orbital.


$\color{Red}{\mbox{red}}$ represents number of electrons (I am too lazy to draw the fish-hooks).
$\color{Green}{\mbox{green}}$ represents $\ce{sp^2}$ orbital.
$\color{blue}{\mbox{Blue}}$ represents $\ce{p}$ orbital.

Note that the two $\ce{sp^2}$ orbitals between sulfur and the two oxygen atoms are in $\ce{\sigma}$-bond.

* The website is no longer available; there is no version in the Internet Archive.