You can ride to Lourdes from Argeles, on a beautiful off-road, highway standard bike path.
Argeles village itself is located right at the base of the Col du Soulor, which if you're looking for a climb you could happily do every day for the rest of your life must surely rank highly.
If the Col du Soulor itself (at roughly 20klm) isn't enough, then just keep going once you reach the top, and head on up to tackle the Col d'Aubisque from the eastern side. Surely one of the most breathtaking roads (and views) in the world.
The Hautacam also starts right at the village of Argeles if you head east out of town on route D100.
I think the day we rode to the Tourmalet it was about 45 klm from Argeles to get to the base of the climb, although we took an indirect route via Lourdes to get there.
I think you'd like staying in Argeles.
Do you really need a fvcking law to tell you not to text & drive?