Of course the simple answer is just "drink what you like", but the truth is that next to eating, socially drinking alcohol is an extremely cultural thing. Therefore it is understandable that there are some gender issues that can come into play.
We might not like or agree with it, but there can be strict cultural rules are built around these sorts of things and people can face consequences (Maybe just getting picked on, or maybe loosing an important customer or even your job) if those rules are not followed. Just feel lucky you are not in a place like Japan, where the unwritten (but strictly enforced) rules about drinking (such as how you hold you glass when it's being filled) can get you into big trouble if they are not followed appropriately.
Since I consider myself a bit of an expert on drinking alcohol (20+ years experience

) I will offer my input.
Here in the US, most people feel that drinks fall into two basic types
sweet and fruity = Girly
Sour, bitter and/or strong = Manly
If you want a "girly" drink just because you don't want to taste the alcohol, there are many alternatives (some listed below) that are basically unisex (just in case you're out in 'guy' mode and don't want people to get on your case). If you want to drink "girly" drinks because they make you feel feminine and you want to express that, then drink whatever you want.
That being said here are some options for sweeter drinks that are basically unisex (or even masculine) in some cases.
-Two ingredient drinks (whiskey and Coke, Seven-and-seven, rum and coke, etc)
-Drinks that don't taste like alcohol (at least not too much) and any bartender worth a darn should know how to make. such as:
1.
Margarita (Everyone knows what this is)
2.
Long Island Ice Tea: This drink was basically designed to hide the taste of the large amount of alcohol that is in it.
3.
Alabama Slammer: Basically tastes like fruit punch, and is also very good at hiding the large amount of alcohol that is in it.
4.
Tequila Sunrise: It's in a song by The Eagles, so I'm pretty sure it's still unisex.
5.
Mai Tai: If you like tropical tasting stuff this will do it
6.
Mojito: Tastes kinka like minty rum and 7-up
7.
Midori Sour: Melon liqueur, but if you put the word "sour" after it, it doesn't come across quite as girly
8.
Bloody Mary: good choice but you need to like tomato juice
9.
Whisky sour: tastes like whisky and lemonade
- If you like the taste of alcohol, but just wan't something mixed here are some options
1. Side car (cognac, orange liqueur) : Basically an orange version of the appletini. Really strong, but sweet don't order if you don't want to taste alcohol.
2. Manhattan: Tastes like whisky but a bit sweeter.
Just remember to Drink responsibly (or you will probably pay for it the next day), and never drink and drive.
Enjoy.
-J