for all the helpful replies I've received already. Keep'em coming.

To clarify a few things: I have only been abroad once, to Ireland. In all the Flyertalk messages I read about Ireland, or anything else I read, I never saw the word "pickpocket." It seems like every thread on France at least mentions the risk of becoming a crime victim. That is why I asked about the camera, backpack and about looking like tourists. But as robyng and jp said, it will probably be impossible not to look like a tourist. It's just a matter of returning with the same stuff I leave with each morning. You can imagine how we'd feel if we had our camera or wallets stolen.

I should also say that Giverny is non-negotiable. This whole thing started in part because my wife and I had a discussion (a la "The Bucket List") about what would you really like to do before you die. She said go to Giverny. I realize it can be swarmed with tourists, but there is no way we are going to France and not going there. My plan is to spend the night in a B&B there and be at Monet's garden when it opens to minimize the number of Americans coming by bus for the day that we have to deal with.

I also did want to get a taste of the French countryside. So far as Burgundy is concerned, I thought a winery tour/tasting would be great and you can't get any more famous for wine than Burgundy. I was also considering Alsace which I have heard is really great for hiking, which we also enjoy, so I was interested to see the plugs for Strasbourg. I hadn't thought about the Loire, but you have really given me more things to think about.

Until robyng posted, it seemed everyone thought the train would be the way to go. A third alternative I am considering: take the train to Rouen/Giverny and return to Paris. Then rent a car and drive to Burgundy (perhaps Beaune instead of Dijon), or the Loire for that matter. We could drive through some small towns. Then return the car to Paris for the remainder. If we were to take the train from Giverny to Dijon, we would have to change stations (St. Lazare to Lyon) in Paris anyway, so I figure we could rent a car at St. Lazare and drive around Paris. I have no intention of driving in Paris proper. That may actually be the most expensive as it is almost as much to rent a car for two days as four.

During the day, do people carry their passports with them, in case of emergency, or leave them at the hotel for security?

About the segways --
When at a new city, it can be fun to take a half day tour to get oriented, and get a taste of it all. We have done that by bus in Chicago and DC, for example. On tripadvisor, I had seen some very positive comments about the segway tour, and I thought it would be a bit unique. The river cruise sounds great too, of course.

So that may give more background on what we are hoping to accomplish. Thanks again.