Covehithe to Southwold is good. Then Southwold to Walberswick, out across Tinkers Walks along the Blyth inland, before picking up the Sandlings Walk (cheeky but few walkers). Inland to Westleton Walks and on to Eastbridge. Sizewell beach is always an interesting visit. Further south, lOts of heath around Thorpeness.
An alternative from Walberswick to Dunwich across Westwood Marshes through the Dingle hills (each about 5-10m above sea level) is lovely but very cheeky and only when VERY quiet. It is however just about my favourite ever walk, across the marshes to The Ship at Dunwich, back along the beach to Walberswick.
I have ridden a lot of the bridle ways and byways on a road bike with 23mm tyres. Sand is an issue but nothing terribly rough. You won’t need an MTB.