The Eurostar is a nice way to arrive in Paris. The Gare du Nord is pretty central in Paris, making it very easy to reach a hotel without taxis or buses. Two of my friends arrived by plane, and they ended up somewhere out of town, forced to take a bus to get to the hotel. We stayed at the Hotel de Rocroy, a nice place close to the Gare du Nord, with a basement vault as its breakfast room.
Paris is a great city for walking. Despite seeming very populated and very densely packed in, Paris has a nice atmosphere to it. Each part of town has a character that stands on its own. For journeys that you don't think you'll survive on foot, the Paris Metro system is a pretty efficient form of public transport.
The city is rammed with historic and iconic landmarks. The Basilique du Sacré Coeur (Basilica of the Sacred Heart) in Montmartre is a brilliant sight in strong sunlight, and its position atop a steep hill gives a nice view of the city lower down. Le Centre Pompidou is a functional building of outlandish architecture, though its interior was less interesting than its exterior. La Tour Eiffel is surely the most famous structure in Paris, but a trip up to the observation decks and back took two of my friends more than four hours, though a lot of that time was spent waiting in the long queues for the lifts. The Arc de Triomphe is another famous landmark, encircled by the most intimidating roundabout I've ever seen. It is possible to pay to go to the top of the Arc de Triomphe, but the view from Champs-Élysées was enough for me. The gothic architecture of Notre Dame is also striking, though I prefer the smoother looks of Église St-Eustache in Les Halles.
In between landmarks, Paris offers a huge variety of bars and cafés, and the culture is very relaxed. Come eleven o' clock at night, the streets are not filled with inebriated teenagers. Instead, the streets are calm and the people are peaceful. There doesn't seem to be the competitive drinking culture that Britain is stricken with. It makes Paris a much nicer city to be out in at night.