Weh is a small island off the very tip of Sumatra. It lays claim to being the northern-most point in Indonesia. The island is part of Aceh province, which fought a decades-long fight for independence against the central government. The 2004 tsunami, which killed as many as 150,000 Acehnese, brought world-wide attention to the province, and in 2005 the dispute was settled, with the province being granted more autonomy from the government.
The diving around Pulau Weh is truly some of the best I've had in Southeast Asia. The numbers and variety of fish seen on most dives is amazing, and the reefs are in excellent condition, with almost no sign of any destructive fishing practices or over-fishing. Although they do get large fish such as mantas and sharks, they can be a bit more rare here than, say, Komodo. Otherwise, I'd put the diving here on par with that much more famous area.
The diving around Weh tends to be a lot more relaxed than the live-aboards that ply Komodo and many other popular Southeast Asian dive destinations. Most dive operators only do two dives a day, with an optional third shore dive in the late afternoon or night. In between dives you can have a leisurely meal (there really aren't any other kind on Weh) or catch some rays on the beach.
To get to Weh, you will end up going through Banda Aceh. The provincial capital doesn't have a lot to see or a well developed tourist infrastructure, but it might well be worth some sightseeing for a day on your way from the island to your next destination. There are several interesting tsunami-related sights as well as some very interesting markets in the city. See my own Banda Aceh travel guide for more information.