Sandown is surrounded by a wealth of natural features and the Isle of Wight is famous for having more miles of footpaths and bridleways than it has roads. Culver Down which overlooks the bay is a chalk down owned and managed by the National Trust, supporting typical chalk downland wildlife and many seabirds that nest on the adjoining cliffs. Much of the down is publicly accessible and offers stunning views over Sandown Bay so is well worth the walk from the town.
Slightly inland (towards Brading from Yaverland) you can explore the area of low-lying land which is one of the few freshwater wetlands on the Isle of Wight. It is, according to the Hampshire and Isle of Wight Wildlife Trust: "a wetland site with grassland, ditches and pools that provide shelter and food for a thriving population of water voles as well as many different birds all year round. Kingfishers are regular visitors to the reserve and in the summer, Cetti's and reed warblers can be heard. At dusk barn owls have been known to hunt over the area." You can find the wetlands by using footpaths that head towards Morton Common and Brading.
Another idea would be to use the cycle path (either walking or cycling) that takes you the Alverstone Mead Local Nature Reserve, an ideal spot for birdwatching. Further inland Borthwood Copse provides delightful woodland walks, and a dazzling display of bluebells in the spring. The "Sunshine Trail" will take you in a circular walk form Sandown out towards Godshill and back via Shanklin, but this is a full days walk if well worth it.
Perhaps most interesting is the designated Special Area of Conservation which covers the reefs and sea bed offshore. At very low tide a petrified forest is partially revealed in the northern part of Sandown Bay, and fragments of petrified wood are regularly washed up on the beach.
View of Sandown from Culver Down.