You don't want a big city, but you may not want something the size of a postage stamp (Beilstein) either. Pretty, but not a lot there. As you can see in the photo below it's roughly the length of 8 tour buses.
Beilstein
I'd prefer to visit Beilstein on a 1-hour river cruise from Cochem, a larger town of about 5,000 residents.
Riverfront in Cochem
Reichsburg Castle in Cochem can be reached on foot from the town center.
Market square
Narrow alleyways
Falconry show on Castle grounds
View from chairlift
A car is not essential here. Trains run hourly or better in each direction and take you to other river towns - like Trier (city, Roman history) Moselkern (for Burg Eltz castle walk,) Traben-Trarbach (wine town,) Winningen (wine village,) Bullay (good place for hiking and biking,) or to destinations on the Rhine (Boppard, St. Goar (Rheinfels Castle,) Braubach (Marksburg Castle.) Some of these trips are much more efficient by train than by car (like Cochem-Bullay, which is less than 10 minutes by train but nearly 40 minutes by car.)
Two adults can get a 3-day train/bus pass (mini-group ticket) for €43.60 to cover nearly all these destinations.
Which airport? Depends where you're coming from. Frankfurt Hahn (Ryanair base) is closest to Cochem. The shuttle to Bullay is 45 min. plus a 10-min. train ride.