Why the atomic (metallic) radius of gallium is less than that of aluminium?
First, you have to look at the definition of metallic radius, which is the half distance between two atoms in a lattice. It has a significant dependence on crystal structure.  


  Tanget relevant to the question and other answers:  Gallium has an orthorhombic crystal structure (CN = 6) whereas as aluminum has a face-centered cubic crystal structure (CN = 12).  This difference in coordination requires a goldschmidt correction to compare values as if gallium were 12-coordinated which makes the gallium's corrected metallic radius actually even smaller compared to aluminum at about $\mathrm{130pm}$.


Gallium exists as a diatomic solid in the lattice, which causes the atoms to be closer together on the  a axis because they are covalently bonded. Gallium's covalent radius is about $\mathrm{122pm}$ which is very much smaller than the metallic radii of either element. This value between the bonded atoms lowers the average distance between atoms giving gallium a lower metallic radius.

If you look at the Van der Waals radii of the elements, (more representative of a monoatomic gaseous atom) you will see that aluminum is actually smaller though not by a lot, giving some credence to the d-electrons explanations, but not a complete explanation in regard to the metallic radius.