Another question as we research this trip:
Is there a good place to stay outside Paris if we want to visit Giverny one day and Versailles the next without a car?

Since both are easily visited by public transport from Paris, staying in Paris would probably be your best bet. (Versailles is essentially IN Paris)

Thanks. That gives us lots of options, anyway. We were just looking for a break from the big city.

You can see Giverny and the town of Rouen (in Normandy) both in a single day trip from Paris, by train. Rouen is a nice town - not a "small town" really but the core makes it feel like one, certainly far smaller than Paris. Take the train from Saint Lazare Station in Paris to the town of Vernon, take the bus from Vernon to Giverny (lots of tourists will go so it's easy to find the buses - tour buses really not public buses).

Giverny will take only a few hours. Afterward, continue on from Vernon to Rouen if you want, spend a few hours exploring the town, then take the direct train back to Paris.

We stayed in the town of Versailles and loved it. We went in the early afternoon, checked into our hotel, had lunch and wandered the lovely grounds of Versailles the whole afternoon. Friends with us even rowed on the lake. We were just about the first people into the chateau the next morning, toured, had lunch, and back into Paris around noon. Rest of day and evening in Paris. It was really nice to get a sense of the whole place before seeing the inside. I have been several times, and that was by far my favorite way to do it.

Staying outside Paris might mean that going to one or the other destination might be more complicated than if staying in Paris itself.

Do you need more than one day for Versailles?

Andrew, that sounds like a good plan. We picked up a rental car in Rouen, but didn't take time to see the town. Might be a good opportunity to do so.

Andrew, I meant to say we picked up a rental car in Rouen on a previous trip.

No, you don't need more than a day for Versailles, but you can easily make it into a pretty full-day trip.

In contrast, I thought Rouen deserved at least a day, if not more!

If the original intent is to see both Giverny and Versailles, I do not think that Rouen is in the picture. I would use public transportation to get to both sites.

(@ Michael -- Andrew suggested seeing both Giverny and Rouen in the same day; the OP said she thought it a good plan.)

If you get a good start and catch the earliest direct train to Vernon, you can get to Giverny fairly early, beat the crowds, and get to Rouen by early afternoon. You can also buy tickets to Giverny online ahead of time, use the group entrance when you arrive, and skip any lines to get in.* You don't need that much time to see Giverny. Note when the buses head back to Vernon and note when the trains depart Vernon for Rouen and you can time it pretty well.

Anyway, you'd have enough time to spend a good long half day in Rouen, plenty of time to get a good feel for it. Just note when the last direct train back to Paris leaves Rouen and don't miss it. (Buy your tickets ahead of time; the trains aren't reserved so you can hop on any direct train back.)

* (Unfortunately, I didn't get going early when I did it; I was demoralized when I woke up in Paris because it was pouring rain; I got on a later train thinking I'd skip Giverny and just see Rouen, but by the time our train got to Giverny it had cleared so I got off and saw it anyway. I had to wait in a long line at Giverny by the time I arrived about 11:00 when the place was already mobbed - this was mid-May.)

I'd like to try your suggestion,Andrew. My challenge the entire trip will be getting those early starts. I'm such a night owl and NOT a morning person, but I'm determined to do better this trip!

Well, it is your vacation, and if you don't get up at the crack of dawn because you were up enjoying Paris late the night before, I don't think it would be the end of the world. I got to Giverny two hours later than originally planned and had to wait in a longer line, but I still did it and still made it to Rouen. I'd say you could stay as late as you want in Rouen too and get back to Paris late, but the direct trains may not run that late. Just check the schedules.

You could make it easier on yourself unlike what I did and buy your train tickets for that day ahead of time: Paris - Vernon, Vernon-Rouen, and Rouen to Paris. They aren't reserved trains as I recall so you can use them on any train (2nd class, at least). If you don't wake up in time for the early train to Vernon, catch the next one, using the same ticket.

I'm not a morning person, either, although I do make a serious effort to get up early enough to maximize my opportunities when traveling.

So, FWIW, I visited Giverny in May. I got there about noon (I rented a car that morning, and although I did get up quite early that day, once at the rental agency, I learned that there had been a mix-up and no car was available, so I had to wait until another arrived....) The iris at Monet's gardens were in full bloom, so the place was PACKED. I also visited the museum of impressionists' work that is also in Giverny. I left Giverny at about 3:30 p.m.

If I had been relying on public transportation, I could probably have gotten to Rouen after that, but I'm not sure I could have gotten there in time to see much of anything before closing hours. If your goal is just to walk around Rouen, it might work, particularly if you leave Paris earlier that I did. If you want to see any of the wonderful things in Rouen that have closing hours, do give some thought to whether the timing works and what you are willing to do to make it happen.

Hope that helps!

The downside of using public transportation for the Paris Giverny-Rouen day trip is that you are at the mercy of the schedule. And that doesn't mean just the trains. The Vernon train station is a long walk (an hour?) from Giverny, so you are kind of at the mercy of the tour buses that run back and forth. Or a taxi. You can find the trains schedules ahead of time of course, but I'm not sure about the schedule of the buses going back to Vernon train station (posted when you get off at Giverny, though).

If you want to see Giverny then head right to Vernon train station to catch the next train to Rouen, you could take a taxi back I guess. I suppose that could save you 1-2 hours if it means you don't have to wait for the next train so maybe it would be worth it.

Another way to save time at Giverny - even if you plan to arrive later like I did - is to buy your entry ticket online ahead of time so you can walk right in at the group entrance instead of waiting for 30 minutes in line like I did. I'm not sure if your entry ticket bought online is for a specific entry time, though. If not, you obviously can't wing it the morning you go like I suggested above.

I think we're going to pass on Rouen this trip. DH has made the hotel reservations in Paris so we will be taking the train to Giverny so now I have another question. I gather we train to Vernon and then bus to Giverny. I understand it's about 3 miles. We are walkers. An hour stroll would be nice IF it's walkable, meaning we won't get run over by cars or buses! What do you think?

I didn't walk it, but I understand it is walkable. (Try googling "walk vernon to giverny.")

If I had plenty of time perhaps I would have tried. I waited a good 20 minutes while the bus at Vernon loaded anyway (they are just tourist buses, not really your typical "city bus"). But I try to save my feet because I knew I'd be doing plenty of other walking. I don't know if it's a pretty walk or not.

You could also take the bus one way and walk back, I guess...

When you arrive at the train station in Vernon go a few blocks into the center of town and you'll see a bicycle lane on the sidewalk. Follow it over the bridge across the Seine and just after that keep following it a few more blocks (as well as the signs pointing to Giverny) and you'll be on a trail dedicated to bikes and pedestrians all the way to Giverny. It is 5km from the train station to Monet's house and gardens. You can also rent bikes across from the train station and cycle there if you'd like.