The size and diversity of the champagne region is vast and there are thousands of places to visit from tiny producers showcasing their wines from little more than a shed to the grand marques with their underground cellars so big you can easily get lost.
There are many ways to visit Champagne but here is how to do it properly. The properties, wineries and cellars of the big names are impressive, they really are, but unless you like repetition I would stick to just a couple (there's only so many times you need someone to explain the disgorgement process). In Reims, I would go for Pommery, it's the birth place of brut Champagne after all and the buildings and gardens are stunning. In Epernay, quirky Mercier is the obvious choice, they are more set up for tourists and have a fun train tour that is worth a go.
When you've got the big houses out of your system, here is how you should spend the rest of your time. Definitely get in a car (hopefully you have a designated driver with you) and take a drive around the Montagne de Reims and cram in as many tastings with houses there as you can (the producers are lining the streets in each of the string of villages on the route). It's best if you book in advance but if you're not great at planning in advance just go around knocking on doors or ring the numbers that are often posted outside. An absolute must is Ployez Jacquemart in Ludes, they have a stunning property and a beautiful tasting room. Be sure to sit firmly in your seat because their champagnes are likely to knock you off your chair; they are sooooo good!!! If you still feel like a drink when you get back to Reims you really must visit "Aux 3 P'tits Bouchons" the ladies in there are simply wonderful people and they really know their stuff.
Once you've slept off the Reims champagne, head over to Epernay where you can take a walk down the Avenue de Champagne stopping off anywhere you fancy. Be warned that most of these places will sell you a glass rather than pour tasters and I didn't come across any spittoons so be prepared to get sozzled. When you've had about as much champagne as you can handle you'll probably need to walk it off. Provided you are able to walk in a straight line and don't have a heart condition you should be able to manage the short hike to Hautvillers, trust me it's worth it. Once there, pay your respects to Ol' Dom Perignon at the church before heading to the top of the hill for a view that will take your breath away (if you have any left). Once recovered, it's probably time for a glass of bubbly you can stop off at various places as you descend but for something light, crisp and refreshing head to Champagne Tribaut, you won't be disappointed.
Finally, if you have any enamel left on your teeth you weren't trying hard enough; go back and do it all over again!