The Pont Neuf is my favourite bridge in Paris for a number of reasons. It’s beautiful to look at from all vantage points, and there are great views of the Seine from on the bridge itself.
It’s located as an extension of the Rue Dauphine not far from the Hotels and cafes I like near the Odeon metro station and Boulevard St Germain, so that’s convenient for crossing the Seine from the Odeon direction or getting home early by hopping off the Metro at Pont Neuf and walking across the bridge instead of changing trains at the busy Chatelet intersection.
But the best reason is because you can go down the steps from the busy road above and enter a nice quiet spot to relax down by the river. On a sunny afternoon there will be a small crowd of people just sitting around enjoying the cool breeze, the view and the tranquility of the trees and small garden, away from the busy city above.
It’s also quite spectacular at night to see the buildings along the banks of the Seine all lit up as you cross the bridges on a warm evening. In the distance you will catch the lights at the top of the Eiffel tower as well, although they are a bit silly these days with colours and flashing.