Absolutely loved the trip from Playa de Las Americas up to El Teide, a 3500metre vertical climb. Loved it so much we did it again to be up the for sunrise, which was quite literally surreal. With complete zero residual light the stars in darkness before dawn were incredible.
Definitely hire a car, don't do an organised trip - you'll want to explore at your own pace. Go up on one road and come down another.
The cable car was €25 return for an adult and €12.50 for kids 12 or under. Pretty steep but it is still worth it. The cafe at the bottom of the cable car serves surprisingly good food and drinks, but make sure you take plenty of water with you, you will surprise yourself y how long you want to spend up there. We were able to see La Gomera and La Palma, then Gran Canaria the other way too!
And the big HUGE piece of advice is to arrange your summit permit in advance - only with this can you get to the very top of the crater to look down inside it. They limit these to protect it from erosion and you can't arrange or even buy one on the day, I was gutted to is this bit. You can do it online here: https://www.reservasparquesnacionales.es/real/ParquesNac/usu/html/detalle-actividad-oapn.aspx?ii=6ENG&cen=2&act=1
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