France

I would spend 3 days in Paris and 3 days in London connecting by using the Chunnel. Forget Amsterdam and Switzerland as you do not have enough time to do justice to either as all you would be doing is traveling. I was in Paris last month for the fifth time and still did not see everything I wanted to see.

Please give me some guidance as how to get around. Do I need a car in both countries? Do I prepurchase tickets. What do I not miss? Thank you. I have 10 days ...3 days in each leaves me with 4 days......should I do wine country....English country....

3 days in London and 3 days in Paris is just an introduction, no time for anything else. 5 days in each gives you enough time for a few (1 or 2) day trips from each. Do not attempt to stay anywhere else.
If you are just going to Paris and London, you definitely do not want a car. It would be about as much use as an aircraft carrier.
For travel from Paris to London use Eurostar. Times and prices at www.eurostar.com

How about 5 and 5, fly into one city and out from the other and take day-trips from each if you want to see countryside. I could spend all 10 days in either city...
Buy your Euro star tickets ahead if time for lowest price. Both cities have excellent transportation systems, car not needed or even useful. Start looking at what you want to visit -- watch the videos online here.

You don't want a car in London and Paris!

Please start by reading Rick's book Europe Through The Back Door. It will give you the nuts and bolts of travel planning. If you have 10 days, you cannot see 4 countries and enjoy them (any more than if you had 10 days for a first visit in the US, you would not want to try to see 4 far-flung states).

You want to think in terms of nights instead of days. Two nights in a city is only one full day; one night is less than a full day. Remember that you lose at least a half day (and often more like a full day) when you change locations. In 10 nights, you can have 2-3 base cities, and take day trips from these if you want. My usual trip is 10 nights, so I do understand the difficulty of cutting things down. For instance, my next trip is to Spain; while I'm still determining the details, I will be spending 4-5 nights in Madrid, 1 night in Toledo, and 4-5 nights in Barcelona. That's it. "But there's so much more to see in Spain!" you cry. Yes there is - and it will have to wait for another trip.

Once you figure out where you want to go, you can determine how to get around. Particularly for a first visit and for one involving multiple countries, a car is rarely a good idea. There are very high fees for renting a car in one country and dropping it in another, and tolls, gas, and parking are very expensive. Furthermore, trains, planes, and buses within Europe are generally excellent and comprehensive (of course, there are exceptions).

You could fly in to Amsterdam, and out of London ...
2 nts Amsterdam
4 nts Paris
4 nts London
However, 5 nts in each, London and Paris, probably easier to manage.

If you're there for ten days, I'd recommend five days each in Paris and London. Take a look at the itineraries on this website for the Best of Paris and Best of London tours. It'll give a very good idea of the highlights for each city.

How many nights in Europe do you have? If you have 10 days vacation, are you using 2 getting to and from Europe?

If your flight lands in the morning, you'll have about 1/2 day on the first day. Many (most?) European flights to the U.S. leave in the morning.

France is only a little smaller than Texas, so I assume you mean Paris (and London). You'll use up 1/2 day getting from one to the other.

You will probably be suffering from jetlag and lack of sleep when you land. Expect to be disoriented and tired on your first day, and maybe even the second one. Dealing with foreign currencies, foreign languages, different modes of transportation are just a few of your hurdles, especially if you are traveling solo. My best advice is don't try to do too much. You may be able to fit in Amsterdam, depending on how many days you really have.

Agree with several previous posts. Five days in London and five in Paris gives you enough time to really start to know those cities. Perhaps a day trip from each but not any more than that. Better to do a couple of places well than many place that will just be a blur.

Especially since the 10 days presumably includes your departure day, which isn't really a vacation day -- it's just a trip to the airport : ( And same if the 10 days includes your arrival day, although usually you can get something out of your arrival day - you'll be jet-lagged, but at least you'll have the afternoon and early evening to wander around, get some fresh air, and see some things.

I agree with the others that you should simply stick to London and Paris, and IF you feel like it, take a day trip from one or both to get a little different flavor (for example Bath from London and Versailles or Giverny from Paris. all depends on what time of year your trip is).