Champagne cocktails are not only a classic, they're easy to make. All you need is sparkling wine (Champagne for preference!), sugar cubes, and bitters (I use Angostura, the only easy one to find these days).
Put a sugar cube in the bottom of a champagne glass or flute; dash on 3+ drops of bitters. Tilt glass and fill slowly with cold Champagne.
Voila. The traditional garnish is a twist of lemon peel, but in a bar you're more likely to get a maraschino cherry.
There are a number of cocktails that include Champagne as an ingredient--the French 75 is my favorite--but this one is the classic.