Where did portugal and spain claim land in the western hemisphere

Basically: everywhere - and not only in the western hemisphere, they claimed all lands that were not claimed by another country that they respected the authority of.

There was actually this very interesting treaty, where Spain and Portugal divided the world (Treaty of Tordesillas), where they divided the world (expect for Europe) among themselves. That left Americas almost completely in the hands of the Spanish, and Africa in the hands of the Portuguese.