In 2013 I went to Paris four times, in May, July, August and October. Each time I stayed in a different part of the city (in the 14th, 13th, 8th and 10th arrondissements) and each time I booked a seven-day Vélib’ subscription, which at that time cost eight Euros (it started at five and has since gone up to fifteen). And I made good use of my Vélib’ subscriptions on all four visits.
This was the year the left bank expressway was permanently closed to motor traffic and opened up for people, including those on bicycles. As part of this transformation, three new Vélib’ stations were installed at the lower quay level of Les Berges (= The Banks): at Port Solférino, Port des Invalides and Port du Gros Caillou.

People on Vélib’ bikes at Les Berges
See also: Re-claiming the river banks.

Vélib’ poster by Adam Turman at Les Docks
Further upstream, also on the left bank, the Center for Fashion and Design at Les Docks had an exhibition of posters inspired by the Vélib’ bikes.

Vélib’ book with sightseeing tours
In 2013 a new guidebook was published — first in French and then a few months later also in English — with suggestions on how to use the Vélib’ bikes for sightseeing “in the Paris of the Parisians”.
The book lists seven sightseeing tours and includes detailed maps for each, showing what there is to see and do, where there are attractive pubs and restaurants along the way, and of course where all the Vélib’ stations were located where you could check out or dock a bike. (As of 2020, most of these locations still — or again — have Vélib’ stations with the same numbers as before.)
The book’s sightseeing tour number 1 goes along the left bank of the Seine from the Île de la Cité to the Eiffel Tower by way of the Orsay Museum and Les Berges.
Sightseeing tour number 2 starts at Place de la Bastille and goes east by way of the City Hall and the Louvre to Trocadero.
Sightseeing tour number 3 starts at the Arch of Triumph and goes west by way of the Monceau Park and Place de Clichy to the Métro station Anvers at the foot of Montmartre.
Sightseeing tour number 4 starts at Place de la Bastille, like number 2, but goes east along Avenue Daumesnil towards the Palais de la Porte Dorée and from there to the Vincennes woods and palace.
Sightseeing tour number 5 starts at La Villette, at the northeast corner of Paris, and follows the canals past the historic Hôtel du Nord. The tour ends for some reason at the Bataclan on Boulevard Voltaire, though there is nothing to stop you from continuing on down to Place de la Bastille, as I have often done.
Sightseeing tour number 6 is the most complicated one, since it zigzags a bit through various parts of the Left Bank, starting at the foot of the Montparnasse Tower and going by way of Saint-Germain-des-Prés to the Latin Quarter, and from there back to the Luxembourg Gardens and Montparnasse Cemetery.
Sightseeing tour number 7 starts at the Bercy Park, crosses the Seine on the Bercy Bridge and continues via Place d’Italie to Denfert-Rochereau.
Confusingly, the numbers of these sightseeing tours from the book are not at all identical with the numbers of the signposted bicycle routes that lead through all parts of the city. Sightseeing tour number 7, for instance, follows part of the signposted route number 4. Sightseeing tour number 1 follows part of the signposted route number 10. (Etc.)
Also, each of the sightseeing tours is divided up into segments which are also numbered.
But aside from all the numbering, I still found the book useful for finding things to see and do along the way.

Vélib’ bikes at Café de l’Échelle
My photos in this post are from 2013. I revised the text in 2020.
Next: Vélib’ 2014.
I too like staying in different arrondissements which I then try to fully explore, though I do now have favourites.