Looking on the internet deeply has found these results:

stay outdoors is the most popular phrase on the web.

stay outdoor 136,500 results on the web	stay outdoors 1247,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
[Then, Signora Franca invited Marta to stay for lunch, outdoors, in her garden.]	[Then, Signora Franca invited Marta to stay for lunch, outdoors, in her garden.]

stay outdoor

136,500 results on the web

stay outdoors

1247,000 results on the web

More popular!

[Then, Signora Franca invited Marta to stay for lunch, outdoors, in her garden.]

[Then, Signora Franca invited Marta to stay for lunch, outdoors, in her garden.]