Actually it's not really a shipyard anymore - just a collection of boats unfit for use even by Sudanese standards! Karima used to be the ship-building centre of Sudan. Not any more. All that's left is some old wrecks on the banks of the Nile. But down by the river is a small beach and a green grassy area. It's very attractive and nice to just sit and talk and watch the world go by.
Beneath Jebel Barkal are the ruins of the ancient Temple of Amun. Jebel Barkal itself was a significant religious site and a temple was built below it. You're free to wander around the temple grounds - there are statues, obelisks, heiroglyphics, many partly hidden by the sand and eroded over the centuries.
A short walk into the desert behind Jebel Barkal takes you to some pyramids. They're not huge but they're still impressive, particularly given their desert setting. Some are crumbling but generally in good condition, complete with graffiti both modern and ancient. Compared to the precise symmetry of Egyptain pyramids these are quite haphazard with wonky walls and different sizes. But that's part of their charm. Ideally walk around at dusk.
When sun set. you don't miss it from the top.
It is not difficult to climb the mountain.
You can get great views.
If you walk around the area near the main souk in Karima (down by the river) there are some interesting buildings to look at. These with the white conical roofs are old kilns.
See my separate Barkal page, but Jebel Barkal is the sacred mountain that dominates Karima and is the town's main reason for being.