Central Tower is in the middle of Hyrule, south of Hyrule Castle. This page gives advice for activating it.
Activating Central Tower
Central Tower is just to the left of Hyrule Castle when viewed from Great Plateau Tower. It is easy to reach on foot after you get the Paraglider, but there are several Guardian Scouts at the base of the tower.
If you want to fight the Guardians, it is recommended to get Guardian weapons and shields from "test of strength" shrines and use those against the Guardians. You can also go to the Hateno Lab in northeast Hyrule to get the Guardian armor set and some stronger Guardian weapons and shields.
It is also possible, but difficult, to avoid the Guardians' attacks as you approach and climb the tower.