Hey, hey, that shop just opened apparently! Wanna swing by?
Literal
Hey, hey, that shop, new-open [hearsay-だって]! Stop-by-[try-てみない]?
Double ね opens as an attention-grabber. ニューオープン is a wasei-eigo compound built from English loans — 新規開店 would be the native formal equivalent. だって reports hearsay ('I heard / they say'). ~てみない '(won't you) try X?' is the negative-question invitation, gentler than straightforward ~ましょう. 寄る 'to stop by / drop in.'