Epernay is located in the center of Champagne and has the most Champagne houses, more than even Reims. It's about 130 kilometers (80 miles) from Paris, about the same distance as Reims, and is 18 miles (29 kilometers) south of Reims - about a 30 minute car drive or train ride away. It is on the bank of the Marne River, on a major train line from Paris, and an easy day trip by car or train from Paris. Some of the major Champagne Houses there include Moet and Chandon, Pol Roger, and Perrier-Jouet (see Champagne Houses in Epernay for details).
Epernay is very much the business center of Champagne, and is the self proclaimed capitol. The vast majority of people in Epernay work in the Champagne trade. Under the streets of Epernay are an amazing 110 kilometers of cellars and over 200 million bottles of Champagne. Champagne Mercier (the most popular Champagne is France) even once teamed up with Renault, the car maker, and had a car rally held partly in its 18 kilometers of cellars - a publicity stunt no doubt, but impressive.
You can stay in Epernay, however many people who visit stay in the surrounding countryside which is beautiful and has several wonderful places to stay. Epernay is a great place to base yourself during part of a stay in the region, and having a car is ideal. That said, the main avenue de Champagne is very walkable and has some major Champagne houses on it,. You can certainly stay in Epernay and have fun without a car, walking and taking cabs. You can also rent a bike at the municipal swimming pool, biking maps are available from the tourist office, and also take a look at Le Pays de Champagne a velo for biking information.
Let's be blunt though: although some may describe Epernay as more charming and certainly smaller than Reims, you visit Epernay because you are into Champagne! Although they do not exactly "roll up the sidewalks at night" in Epernay, there is very little if any nightlife. There are far fewer restaurants, bars, and bistros than you would expect. Many close up early, or as some people say, have "farmers hours." Tourists do not go to Epernay, Champagne aficionados and people in the trade do. Unlike Reims or Troyes, there just is not much besides the Champagne to see or do.
If you are just doing a day trip from Paris or even 2-3 days, Reims is a better choice all other things being equal. For a multiday trip to Champagne, Epernay is well worth visiting. You can take a day trip from Reims (car or train), stay in Epernay, or the beautiful surrounding countryside if you have a car.
Remember that Champagne is a rather cool region so bring warm clothes. Also, unlike many parts of the world, France is more formal and for example many of the nicer restaurants require men to wear jackets (unlike for example Boston, where current no restaurants require that any more!). Champagne cellars are also quite cool - jackets or sweaters please!