For champagne, drive to Reims and park the car until you are ready (and sober enough) to drive. The town is mostly walkable, there's good public transport, and you can take the TER train to/from Epernay for more tours and tastings. Reims is where most of the cave tours are. The smaller ones may only have weekend hours and may need to be arranged in advance. The TI is very helpful with both providing info and helping to make arrangements once you're there.
I toured Tattinger and Martel in Reims (close to each other) and Mercier (the most fun) in Epernay. My visit was in late April. The TI booked the ones in Reims for the same day I arrived and Mercier was a walk-in, as are quite a few in Reims. Now that I think of it, I think Martel may have been a walk-in as well.