I ended up on this post from Google, and Lucas Kauffman's answer is wrong.
"The root port is always the link directly connected to the root bridge".
That's not true. Look at the following topology :
STP
Multilayer Switch 1 is the Root bridge. You can see that Multilayer Switch 3 is directly connected to it, but its port is blocked nonetheless. That's because Multilayer Switch 3 is connected with a FastEthernet link to Multilayer Switch 1, whereas all other links are Gigabit Ethernet links.
So, the shortest (least hop) path is NOT selected for the Root port, even if directly connected. You should always calculate the cost to the Root Bridge. In this case, 2x Gigabit links give a cost of 4+4 = 8. The FastEthernet link has a cost of 19. Hence, the Root Port is the link towards Multilayer Switch 2.