A big sunny day is perfect for airing out the quilt.
Tips
grammar
大 + weather noun is a common colloquial pattern to intensify: 大晴天 (clear sunny day), 大雨天 (big rainy day), 大雪天 (big snowy day), 大热天 (blazing hot day). The 大 adds scale and everyday emphasis.
culture
晒被子 ('airing quilts/bedding in the sun') is a classic Chinese use-case for 大晴天 — bedding is routinely hung over balcony railings across China on bright days to kill mites.