Itinerary for late afternoon arrival to Paris from London

An orienting walk would be a fine first evening, but the Latin Quarter on Saturday night will be good only if you like cheap kabobs and tourists packing the sidewalks. If you want to save the big must-sees then consider a walk around Ile Saint Louis and the back side of Notre Dame, keeping an ear out for low-key socializing on the banks of the river, and then continue up to the Hotel de Ville and then on to Place des Vosges. Nice evening meals to be had in cafes in the Marais. Livelier party opportunities also available in this area if you have the budget.

I dunno the answers for the other questions but here's an answer to one you didn't ask.... be at St Pancras ready to check in a full hour or more before your departure time.

You have to meet check in deadlines - strictly enforced - then airport style security, then UK departure control then French border control, and if you are late you don't go.

Paris has six large train stations serving different directions of travel, not one main one. So your Eurostar from London will arrive at Paris Gare de Nord, your hotel may be near Gare d'Austerlitz, and if you're still planning on a train to/from Italy or Swtizerland, they will use other stations. So the first step in Paris will be taxi or public transport to your hotel.

Thank you for the ideas and thank you for the heads up about leaving out of London. I did not know that. Also, I understand that I need to get transportation to my apartment. That's why I asked about what to do in the evening that would be something simple. Thanks for the comments everyone!

If you have Rick's Paris guide book or his App, you could do his Historic City Walk which starts in front of Notre Dame and wends around the area.

http://www.ricksteves.com/watch-read-listen/audio/audio-tours/paris

I always recommend strolling the Ile St. Louis and de la Cite first thing when in Paris for the first time. After that you can go over to the Marais, where there are many restaurants and bars. Both are among the most picturesque areas of the city, and the islands and the river are beautiful at sunset. I highly recommend them over the Latin Quarter. The Montparnasse tower view is nice, not sure I'd recommend going there first night. The view is great, but the building itself and the area is not so much.

Idea #1 - Late afternoon stroll through the Luxembourg Gardens, then through St Germain to the Seine and see the illuminations come on to Notre Dame. Dinner in the Latin Quarter.
Idea #2 - Explore the Ile St Louis, then perhaps a visit to the Pompidou Centre (open til 9pm). Dinner in the Marais.

We always take a taxi upon arrival on the Eurostar even though we know the metro and visit Paris annually. It's around 20 euros to anywhere in central Paris. The ride door to door across Paris with all the famous monuments in view is worth the cost of the taxi. Print off a copy of your hotel's website, with the address, to hand to the taxi driver. You can purchase a carnet of 10 Paris metro tickets at the departure lounge at St. Pancras, the Eurostar station in London. You can also buy a carnet (or two) onboard the Eurostar in the snack bar carriage. We stay on the islands and we always take a leisurely walk around on our arrival day, grab a crepe from a street vendor, and watch the crowds in the Notre Dame courtyard.

Consider a Fat Tire bike tour of Paris after dark, or the more expensive Segway tour. They're fun and it will help you get oriented.

Rue Mouffetard is always worth a stroll. It is one of the few Paris streets that was not straightened out by Baron Haussmann's massive urban reconstruction in the 19th Century. Full of life (and tourists) although the Saturday street market will probably be closing up by the time you could get there.

Wow thank you all for the wonderful ideas!