Tenerife without a car is doable. Tenerife with a car is a different island. The guaguas (buses) cover the main routes, but for Masca at sunset, the hidden coves of the northeast, or the Teide road via Vilaflor at dawn — you need a steering wheel. The good news: prices are among the lowest in Europe. Budget 15-25€/day off-season for a compact car, often less than an Uber from the airport to your hotel.
Both airports (Tenerife South for the touristy south, Tenerife North for the authentic north) concentrate all the rental desks. Local companies dominate: Cicar (Canarian, the most reliable, recent fleet), Autoreisen (good value for money), and TopCar (everywhere but variable service). International chains — Europcar, Hertz, Sixt — charge 30-50% more with no real advantage on an island 80 km long. Avoid ultra-discount rental companies without a physical office: hidden fees (cleaning, fuel, scratches) skyrocket at return. The trick: book online 2-3 weeks in advance, especially in July-August and Christmas. Prices on-site are always more expensive.
The TF-1 (south motorway) and TF-5 (north motorway) are free, well-maintained, and fast. It's between the two that it gets tricky. The TF-436 towards Masca is famous: hairpin bends, no guardrails, and tour buses coming head-on. Not dangerous with a compact car and a bit of nerve — but motorhomes suffer. The TF-21 from Vilaflor towards Teide is the most beautiful road on the island: pine forest, volcanic desert, view of La Gomera, all in 30 minutes. The Anaga roads (TF-12, TF-134) are narrow and misty but spectacular. Diesel costs about 1.10-1.20€/L — much less than in France. Note: gas stations in small villages close on Sundays.