When I go on a trip I prefer to stay close to action. It saves on bus or metro fare and I can stay out later in the evenings. If you are looking for evening entertainment I suggest looking for a place in the 4th or 5th Arrondissement. Many locals and visitors hang out along the riverside in the evenings for dancing, music, and street performers. Your dining and bar options are plentiful here. 

For a quiet cafe and view of the Eiffel tower I suggest the 7th Arrondissment. For tourist attractions the 8th Arr. is the place to be and the Luxembourg gardens are in the 6th. I suggest staying close in the city center. Around the perimeter there isn't much to see and can be a little interesting in the evening. However, I will say I have never felt safer in any city than Paris.

If you want a view of the city try the 18th Arr. in Montmartre Hill. There are lots of galleries and cafes to enjoy. So romantic ! It's perfect for lovers. 

Detailed information can be found here on this website View on Cities.