The best replacement for martini is manhattan.

The best alternatives to martini are rated as following:
★★★★★  manhattan
★★★★  margarita
★★★★  dry martini
★★★  gibson
★★★  dirty martini
★★★  cosmo
★★  martini
★★  cocktail
★★  diaper genie
★★  cinzano
★★  kompella
★  revel
★  beego
★  noilly prat
★  mojito
★  diaper genies
★  vermouth
★  regular martini
★  vodka martini
★  tortora
  wine calories
  vodka
  extra dry martini
  cosmopolitan
  gin martini
  ofbiz

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Speaking about martini, one probably shouldn't forget about olive.

Other search terms related to martini and their ratings are:
★★★★★ olive
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Google Trends

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martini
manhattan
margarita