Mint adds a freshness to drinks that's hard to duplicate with other herbs, but if you don't have access to mint or don't want to use it, you can let a few other flavoring agents stand in. These herbal substitutes provide interesting and sometimes unexpected flavors, but don't expect them to duplicate the cooling pungency of mint leaves.
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Basil is a member of the mint family and can stand in for mint leaves in drinks such as mojitos, lemonade and iced tea. To make a mojito, muddle several fresh basil leaves with superfine sugar. Add one part lime juice for every two parts rum and top with a generous splash of club soda. Sweet, anise-flavored Thai basil is particularly well-suited for this drink.
Although tarragon can't replace mint in a classic julep, you can add the fresh leaves to iced tea or lemonade for a licorice-y bite. Tarragon possesses an intensity that could overpower a drink if you're not careful, though. Add just a few leaves per pitcher, and recognize that for some, its flavor is off-putting.
You may be most familiar with the scent of lavender in soaps and sachets, but its mild, herbal essence can also add flavor to drinks. Use a sprig in lemonade or iced tea instead of a mint leaf. Too much lavender can make a drink bitter, though, so use restraint.
Shiso, an Asian culinary herb also called perilla, provides a flavor that hints of mint mixed with basil. If you can find it, make a twist on the classic by muddling fresh shiso leaves with a Thai red chili. Mix this combination with cucumber slices, simple syrup, lime juice and rum. Thyme, another member of the mint family, offers an herby alternative to mint in lemonade or iced tea. Fresh lemon verbena infuses cocktails, teas and spritzers with a citrusy perfume and a taste distinctive enough that you won't miss the mint.