Do you realize that there is a hefty cross-border drop-0ff fee on rentals. Check with www.autoeurope.com to see if a car can be dropped off in Strasbourg for the German part of the trip and picked up in Strasbourg for the French part. Of if this applicable to the Basel airport which is, officially, and tri-country airport as it is called the Basel-Mulhouse-Freiburg airport.

What to see from Strasbourg to Paris: Part of the Alsatian wine country, the le Corbusier Ronchamp chapel (http://www.flickr.com/photos/mksfca/4860709437/in/set-72157624529919999 ), Nancy for its Place Stanislas and its museum, Troyes with an interesting tool museum, Provins as a walled town, and others. It might be useuful to read a guidebook such as the Michelin Green Guide for that area.

Thanks Michael for your response, we will be renting a car in Cologne, driving to Paris, Brussels, Amsterdam and return the car in Cologne. I definitely will read a guidebook. Do you mean there is a fee to cross each border? thanks for your help! Any more suggestions where to stay outside of Paris but close enough to take a train or the metro system?

"We will be flying into Cologne, renting a car and staying near Baden-Baden."

Are you driving from Cologne to the Baden-Baden area on day 1? Most travelers advise against long drives like that after transatlantic flights that can leave you drowsy/jet-lagged. Cologne is a nice place for a day. You might also be interested in the castles and villages just south of there in the Middle Rhine Valley:

http://www.welterbe-mittelrheintal.de/index.php?id=288&L=3
http://www.welterbe-mittelrheintal.de/index.php?id=274&L=3

"...we will be renting a car in Cologne, driving to Paris, Brussels, Amsterdam and return the car in Cologne... Any more suggestions where to stay outside of Paris but close enough to take a train or the metro system?"

Because driving into, out of, and within (as you have figured out) these cities is a good bit of trouble, because parking your car in these cities (even at your hotel) can be pricey, and because your rental fees will be going toward an idle car most of the time, it's usually advisable to use the train for these destinations. Advance-sale tickets at www.bahn.de from Cologne to Baden Baden can be purchased for as little as 29€; the same price is possible between Baden-Baden and Paris, and Brussels - Cologne goes for 19€.

Where to stay: Adorable Gengenbach isn't far from Baden-Baden and is a bit closer to the Black Forest most visitors want to see. Outings by train are free since G'bach participates in the KONUS program:

http://www.blackforest-tourism.com/konus
http://www.black-forest-travel.com/places-of-interest/black-forest-railway.html

Link to Gengenbach: http://www.stadt-gengenbach.de/en/tourism/old-town/

Driving between Paris and Brussels: if you are taking a direct line between the two, Lille is a very pretty city in the Flemish style. A really nice spot to take a break. Unfortunately the scenery between the two on the road (particularly around Arras) is pretty blah, so if this is important to you (as it might be), you might consider a different route. The roads through the Ardennes are pretty (the French side near Bouillon is pretty, the Belgian side a little less so, but still authentic little villages) but it's not a very direct route.

Lavandula

You ask about where to stay outside of Paris. Do you mean to stay IN Brussels and Amsterdam? If so a car is worse than useless. What will you do w/ the car while in each city? And staying outside of the cities simply so you can have a car - that sort of defeats the purpose of visiting Paris/A'dam/Brussels. It is usually MUCH better to stay in the city centers.

Trains make more sense (faster and cheaper) - unless you are leaving out some details of why you need/want a car.

No fees for crossing the border, only if you drop the car off across a border.

Instead of Lille which is pretty large, consider Arras which might be more manageable.

http://www.flickr.com/photos/mksfca/4819157857/in/set-72157624436592493

Technically, it is no problem at all to drive to Paris from Baden-Baden and stay outside the city somewhere in the Eastern Ile-de-France with easy and fast access to Paris by RER trains.

Google Etap hotels, Formule 1, or Campanile - which are some of the largest chains that offer US-style motel accomodation, usually outside the city centers with either free or moderately-priced parking on location.
As you can imagine, these locations are usually far less scenic than staying in a nice quaint hotel somewhere in the heart of Paris.

But there are dozens and dozens of these type of hotels in the Ile-de-France, all the way from the Eastern edge of the conurbation (roughly where A4 coming from Strasbourg hits A104 beltway) to the Peripherique. As a rule of thumb, you can say that prices go up the closer you get to the Peripherique).

Same for Brussels (roughly as close to the center as Ring 0 orbital motorway), or on your way to A'dam in the Hoofddorp area along A4 motorway coming from Bxl. By numbers there are fewer than around Paris, but still no problem to find them.

The upside may be that you can save a lot of money (with rooms starting at €40/50), and that you can keep the car.

You will lose a bit of time to commute in and out every day, compared to those who stay in Paris and just have to take the metro to the sights.

OTOH, this way of travel would only make sense (IMO!) if you had a strong focus on seeing the countryside in between your destinations. And the big cities were just something you wanted to see for a day or two as you went from Alsace to Normandy or to Bruges.

Otherwise you could think about renting a car in Germany, explore Black Forest / Alsace. Drop car in Germany, and use trains for the rest of your journey.

IF the car was a non-negotiable MUST, I'd book a Etap hotel (or similar) along the Eastern Peripherique.
These may cost a bit more than those further away and may charge a moderate fee for parking. But you'd usually be connected to the real metro network (not the suburban RER system) in walking distance, with quick and easy access to the single digit arrondissements. And pay less for your trip into the city center as you can already be in the central Paris tarif zone (which needs to be checked for each motel location, if the nearest metro station is).

Thank you all for the great information! Its a lot to research, but our reasoning behind driving a car is to explore outside the cities as well. The car will not be useful in Paris or Amsterdam, except for an excursion or 2 during our stays there. I really do love the idea of taking trains. Cathy