I've always been a cocktail person.
N.B. Different bars will make their cocktails slightly, well, differently. This is only a guide to what cocktails are typically vegan.
Long Island Iced Tea
A medley of several types of alcohol, everything that goes into this cocktail is vegan (luckily, as a lot is mixed into it). Cola, tequila, gin, vodka, triple sec, sugar, bacardi and lime.
While this frothy cocktail might look like it has some kind of dairy mixed in, it's actually free of daitu (and any animal-product)! Usually made with a coffee liqueur, a shot of coffee, vodka and topped with coffee beans (though some places add a dusting of chocolate powder so ask to keep it off).
I'm a snob when it comes to margaritas; and only order them when I'm in a classy upmarket bar. You see, they're meant to be blended with ice but many cheaper bars skip this step. And then there's the taste of cheap tequila. I can drink cheap rum and I can drink cheap vodka but NEVER pass me cheap tequila - it could be the last thing you do. Saying that, margaritas will likely be vegan; even if you're drinking a cheap (and not properly made) one.
It's vegan but you won't catch me drinking one unless I'm in an upmarket bar because of the aforementioned point: how can people drink cheap tequila?
Just like the espresso martini, a piña colada looks like it would have dairy in it and just like the margarita it needs to be blended for it to taste just right. The ingredients are pineapple juice, white rum, and coconut cream - good to go!
Saving the best until last; this is probably my favourite cocktail. A mix of cranberry juice, lime juice, Cointreau and vodka - make yourself the fifth member of Carrie's girl gang.
Try and avoid
A mimosa is a cocktail built on Champagne, so just like it's wine-based cocktail friends above it is out of the vegan pub-crawl for a very similar reason.
The base ingredient of this manly cocktail is whiskey - an alcohol that will sometimes be filtered with animal ingredients. When drinking at home you can ensure you use a vegan whiskey, but out at a bar you can just never know what whiskey they chose when designing the menu.
Another whiskey-based cocktail, which makes it too risky a choice when trying to drink vegan. Manhattan's also contain red vermouth - another type of alcohol that can or can't be vegan.
Just like the Manhattan above, this cocktail contains vermouth. Sometimes vermouth is vegan, sometimes it's not. It's a risky one.
I've never had a Bloody Mary in my life; the whole concept just sounds...unpleasant. Even before I went vegetarian I never had any desire to try one and even if I did develop that said desire - I wouldn't be able to act on it (unless I made them at home). Bloody Mary's contain Worcestershire Sauce and it's a little known fact that this sauce isn't even vegetarian (let alone vegan). But psssst, there's a vegan Bloody Mary in the 13th Note if you are so inclined.