Best place to eat ( all the locals do so you may have to wait for a table) is 'La Toscanina' in Monmarte - nearest Metro stop is 'Brochant'. Truly hope that this owner run, small,fab, reasonably priced bistro/restaurant is still alive and well. Haven't been for a few years.
As far as seeing - go with the flow - things just pop out at you in Paris - something to suit all! Have fun....like the song says, "I love Paris in the Springtime........etc.