Hmmm...travelling alone. Keep your money and passport in one of those things you carry around your neck. But keep it under the shirt so you don't look like a tourist. Don't accept drinks from anyone, they're after your kidney. But above all, avoid the Paris metro after dark. Avoid it like the plauge.
If you want to visit the Eiffel tower, keep in mind that it takes all day just to get up and down again. The lines are so long. Don't try to walk the first two stages, your legs will cramp up. But the view is worth it!
I only had one day in Paris, but "La Defence" was quite impressive. That and the Eiffel tower was all I had time for. The Metro is one of the great mysteries of the modern age. The lines go like a pile of spagetti. There is no timetable, the trains just...run.
Or you can just come and visit wonderful Copenhagen. The riots are almost over now.