How far is the Eiffel Tower from Charles de Gaulle airport?

Q:
I have an overnight layover in Paris arriving at 8pm and leaving at 9:30am the next day. I would like to visit the Eiffel Tower and any other attraction that would be open during these hours. Is this possible? Can you suggest best form of transportation and approximate costs?

A-1:
The Eiffel Tower is about 26 miles (42 kms) from the CDG airport There is a metro (rer) from the airport but you will have to make some connections. Best way would be a taxi. Taxis are on meters and should run round trip about 100 --140 euros, The eiffel tower has a nightly light show. You probably will miss it. At the time you will be in Paris all the attractions will be closed. You can stroll down Champs Elysee and people watch or go to one of the club areas like Montmartre or if you have time just stop in one of the late night bistros. Paris is not that large a city and most areas can be reached by taxi or metro in a short time.

A-2:
From the moment you step off the airplane, it will take you about 2 hours to get thru "stuff"; (baggage/customs/ make train/metro transfers) to finally sit down at one of the benches at the base of the tower. The night show is good and the place is barren of most people..it is a good time to watch without having to beat the crowd (check out how the top rotating light is actually 4 lights which turn on and off in sequence). I got off at the Berkhim(?) stop and walked along the river until I came to the Eiffel..then I walked the Champ de Mars (there are several bathrooms there) and saw only 2 couples. You won't be able to hit the place during the day because of your early departure.
You will probably want to check into your hotel first. The train and metro are good..where are you staying? If you study the metro map, it is probably faster than a taxi. There is less traffic at night, but I still think the metro is best.
If you only have a backpack..maybe it's best to to do the Eiffel first, possibly hit the Arch of Triumph and then walk all the way down to the Louvre and maybe cross a couple of bridges. You might find a street vendor selling roasted chestnuts. You can reverse your direction using the metro and go see the Grand Arch at La Defense (you need a metro ticket each way; buy a carnet of 10 tickets before the windows close..maybe buy them at CDG). Montmarte is lively until 1am-ish..use the Anvers stop for the Sacre Coeur (very high spot..sit on the steps and see the city). The metro stops about 1am so plan to do most of your far searches first and then do the areas around your hotel..unless you get a taxi from a late night bar. There are some clubs which stay open till 6am. Stay away from the Barbes-Rouchechoart area!
Next morning: going back via metro and train, it will take 1-1/2 to 2 hours to find yourself sitting at your gate with time to take a breather before almost immediately boarding...take the 2 hours and you will be sure to catch your flight.
Bring Euros from your home bank to save time.

A-3:
The absolute earliest you will be able to get into Paris is around 10pm and it might be tough to get tickets to go to the top.
As Nars said, Sacre Coeur in Montmartre is a great place to visit at night. The Basilica may be closed by the time you get there, but the view of the city at night is well worth the trip to the top.
BTW - the metro doesn't go to CdG. You can take the RER B line and then hop onto the metro...

A-4:
We had seven hours to spare at Charles de Gaulle between flights, so took the metro into Paris, €9.10 each way. It took an hour and a half, including a short walk from the station (Gare du Nord/Tour Eiffel) to the Eiffel Tower itself. It was daytime, and there were long queues. By the time you have collected your luggage and got to your hotel, it will be at least 10 pm. The Tower is open until midnight June - September.
If you are taking the metro back to the airport, watch the screen showing the next destination. The line forks and not every train goes to the airport.
The train we were on was heading for terminus B5, and Charles de Gaulle is at B3, but we were lucky to spot this at an earlier station (before it diverted) so got off and waited for the next train. If we hadn't noticed, we might have missed our flight.