Anyplace means in or to any place at all. Go anyplace, anyplace warm, not anyplace near.
It is American and informal, and anywhere is the standard word everywhere else and in careful writing. It is written as one word in this sense, where any place as two words means any particular place. The pattern matches someplace and no place.
1adverbanyplaceIn or to any place at all.
“You can sit anyplace you like; the seats aren't numbered.”
anyplace is a place.
Also accepted in games: wherever, anywhere
Any plus place, formed on the model of anywhere. It is an American formation of the nineteenth century.
From any + place.
Etymology from Wiktionary, CC BY-SA