In contrast to the rockier west coast of Izu, the east coast has more sandy beaches. This is strikingly evident with Shirahama [白浜], about 4 km north from Shimoda. You will notice the mounds of white sand as the road dips you down and around. I've heard that this beach is man-made, that it is not; in any event it's beautiful, has surfing, and is crowded with the 'see and be seen' set in the summer months.
About 9 km further on, to the right, is the more sedate 'Andy Land' [アンデイランド ]. It is a reptile house that contains turtles and reptiles, mainly the former. I never miss the chance to turn off here. After you tour the interior, you can walk out the back into a courtyard; behind that is a trailhead with a wooded path that leads you down to a rocky coastline. If you're into tidal pools this is the place for you. Just remember to bring strong aqua shoes, and if you must snorkel in the larger pool be wary of the incoming tides.
Just north of Andy Land on your left is route 14, turn left if you are in the mood for a hike. Go about 10 km northwest, merging with route 414, and just before you reach a mighty corkscrew of a road is Kawazu Seven Falls [河津七滝]. The hike is more challenging than meets the eye, as the water is cold and the river fast, so be careful not to fall in.
After heading back to coastal road 136 and turning left, go about 4 km and on your right, behind a hotel, is Imaihama [今井浜]. This is a bathing as well as a surfing beach with a sandy bottom, public access, and relatively easy parking.
About 14 km north of there is Akazawa [ 赤沢], prized for its large hot springs resort high up on the bluff which affords a magnificent ocean view. To the right of the resort and down below is a small, black-sand beach with occasional surfers and a small, outdoor hot-spring bath that is free.
A few km north of Akazawa on the right is Jyougasaki's [城ヶ崎] Izu Ocean Park, which has arguably the best scuba diving on Izu. There is a reasonable entrance fee. The park is verdant, with an adjoining, but separate, flower garden and a seaside chlorinated pool. The scuba diving is a dog-leg right with lots of fish. I have seen large squid here in the flats, and if you really want to kick hard, there is a large pillar at the far reach of the dive that is teeming with life, just remember that you need to get back and make that ninety-degree left turn back to the beach.
As experienced water enthusiasts know: the power of mother nature in her liquid form is nothing to be trifled with, on the contrary, it is to be respected always. Use your judgement, gauge your abilities, interact with the locals, and have fun on the Izu coast!