It might be $30, but that's still a steal. I hate bars/their prices. So I'll re-ask what are some good cocktails to try?
Depends on your palate, and the barman's mixology style. Some go heavy on the booze, others light. Some drown a martini in vermouth, and others (properly, imo) will put some in, coat the glass and discard the excess.
for sweet drinks that tend to mask the alcohol, most anything mixes well with vodka. Screwdrivers (vodka & OJ) Cran & Vodka is an old favorite of mine, especially if the cran isn't too sweet. I find the tartness of the cranberry masks the alcohol very well. Spiced rum & coke is always good, and Seagram's 7 and 7UP are generally our bar standby if we run out of ideas.
Personally for a more "sophisticated" drink, I love Gin & Tonic. I prefer a very aromatic gin like Bombay Sapphire, but you might prefer a less obvious gin.
and for god's sake if you get a martini, do it properly, gin, not vodka, with just a small amount of dry vermouth, and of course slightly stirred. I hate all these people thinking they'll be cool and original if they order a drink like they're Bond.
Some "heavier" drinks I like (as they both include cream/milk) are Paralyzers and just like the dude, White Russians.
If you want something palatable that will get you screwed up quick, a Hurricaine or Long Island Iced Tea will get you there. I'm not even going to try on the recipes for these because i've only had them if a pro is mixing.
Something i've been meaning to taste-test for a while is OJ, Cran, vodka and Beer. It's great without the beer, but I think the extra fizz would be nice and take the sweetness off the OJ/Cran that all too often are loaded with added sugar.
If you're feeling a little more vegan, A bloody mary or ceasar might be up your alley. The acid and salt really pops the taste buds.