Once stayed in the car park below Whitsand Bay Hotel, Port Wrinkle. It might be a Bit further out than required but has lovely view to wake up to. You pay the man in the little beach cafe there. Think it cost us £3. Beach right below you, it's lovely.
I think the car park off Mutley Plain (near the railway line and old Royal Eye Infirmary) has 24 hr parking. Might be worth trying the train station too. Otherwise, you should be able to find street parking within a 20 min walk of the Hoe.