I am catching the Tour in Nice on Stages 20 & 21, so I haven't studied the routes/host cities outside of those places, but just looking at your list, I would say Pau would be your best bet. Pau is an historic tour town (if I remember correctly), and with it ending one day AND beginning the next day there, you will be able to get a taste of MOST of the types of excitement. The finish and the awards at the end are neat to see as well as the next morning when the riders are getting ready and warming up and you could even meet some of them if you wander over to the buses. Not really any exciting racing happening right at the ceremonial start, but being in a start/finish town is the best of both worlds!
July 14th is Bastille day which is always a fun time as more folks are off work and out on the course, and the fact that it is Plateau de Beille (a famous mountain to ride-for the sheer fact that I remember the name haha), that seems like there will be some "fireworks" that day. Getting up the mountain will be way harder on that day, but when they go up a mountain, they go slower. You will be able to see more of the action as they are fighting their way up a hill instead of speeding past you at 30km an hour in about 3 min on a flat road. People start staking out their spots on those mountains DAYS in advance though. I bet lodging is maxed out already in Pau, but if you have a car and are nearby, it might be fun to figure out how to get there and see it.
I was glancing at the road book for last year and there was a depart from Pau....this was the info included:
PAU
Prefecture of Pyrénées-Atlantiques (64)
Population: 75,700 (Palois and Paloises), 162,000 within the 31 communes
comprising the Pau Béarn Pyrénées municipality
pau.fr
Tour de France: Stage town for the 74th time. In 2019, the centenary of
the appearance of the yellow jersey was celebrated in fine style in the
capital of the Béarn. The anniversary was marked in the most beautiful
way by Julian Alaphilippe, who won the Pau time trial while wearing the
yellow jersey.
Cycling: 25km of cycle paths and 101km of cycle lanes, Idecycle (self-
service bicycle rental, electrically assisted bicycles, tandems and
children’s bicycles, 170 bicycles in 15 stations)
Sport and culture: Section paloise (rugby, Top 14), Élan béarnais Pau-Lacq-
Orthez (basketball, French championship), Pau FC (football, Division 2).
Athlete: Tony Estanguet (canoe-kayak, triple Olympic champion, president
of the organising committee of the 2024 Paris Olympic and Paralympic
Games).Facilities: White-water stadium, skate park, jaï-alaï, Basque
pelota complex. Events: Teréga Open Pau-Pyrénées (tennis, ATP challenger
tournament), Motor-racing Grands Prix, International Three-Day Eventing
Sights: Château (12th-19th century, birth place of King Henri IV) and its
national museum, Museum of Fine Arts, Bernadotte Museum, Palais
Beaumont, Saint-Louis Theatre, 19th century English villas, Tour des Géants
(open air museum dedicated to the Tour de France)
Gastronomy: Garbure (meat and vegetable stew), foie gras, poule au pot
(chicken stew), Jurançon wines
Distinctions: Fébus (France’s first hydrogen-powered high-speed bus in
operation since 2019), 4-star floral city
