「今週からプール開きね」「そっかー。じゃあ、水着買いに行かなきゃ」

「」「。、」

'The pool opens this week.' 'Oh right. Then I need to go buy a swimsuit.'

Literal

'This-week [from-から] pool-opening [confirmation-ね]' 'Oh-right. Then, swimsuit buy [purpose-に] must-go'

プール開き 'pool opening' is a seasonal event — the official start of the swimming season at schools and public pools, typically in June or July. 買いに行かなきゃ contracts 行かなければ into the casual なきゃ, expressing obligation: 'gotta go buy.' Seasonal school-life dialogue.