Paris is a great city to get lost in. Grab a map from any concierge in any hotel and hoof it around the streets. All the major cool stuff is within walking distance of the center of the city. Stop often to have wonderful pastries, visit the major sites, and take your time to drink it all in. I hate doing "touristy" things, but there is something about Paris that makes it all okay.

There is nothing to be afraid of while walking around. It's all perfectly safe and sometimes getting lost is the best thing that can happen.

I recommend a trip to the top of Notre Dame (to get on the roof) so that you can get a great view of the city. I don't know if the line to go to the top of the Eiffel is worth it, unless you just really want to see Paris from that high up... the Notre Dame view is more interesting to me.