Aksum both surprised and disappointed me when I visited there in June of 2006.
First of all, we saw these tombs that were similar to the tombs in the Valley of the Kings in Egypt, but without the hieroglyphics and ornate carvings. Still, very interesting.
The guide told me that 83% of Aksum was not yet surveyed because of poor funding. British and International archeologists are busy cleaning up sites, digging out tombs and preparing the way for tourists.
Three or four of the sites were not yet open to the public. One opened 2 weeks after I left.
The stelae park was well worth the visit, and in a few years (once again-funding), the stelae that the Italians stole and then gave back will be constructed just like it was in Rome.
Across the street was the church of St. Mary. It is a modern church, but I had the privelege of seeing their enormous 300 year old bible. Fantastic. David Lewis is right, the church where the ark is supposedly held is not so great. Though learning about the controversy is quite interesting. I have researched it and most scholars actually do trace the ark to Ethiopia...but then again, that's only if its still around.
The museum was interesting, but only at 10% capacity (they had about 20 tin sheds on the property chock full of ancient items from the area). The museum is being built behind stelae park.
Our guide took us to some shack far away from the city and inside was a type of "Rosetta" stone. A tablet with ancient greek (big hit with me), G'iz, and...something else. Tourists are apparently allowed to trace over it with paper if they wish. I wish I would have known about this place before I went, I would have brought something to copy it with(the tablet itself is hard to read).
Lastly, Queen Sheba's palace (if Sheba did indeed live there--our guide explained that many scholars doubt she ever existed) was like Hadrian's Wall in the UK. Various kinds of rocks stacked on top of one another and a few rock tiles. The guide told me that the locals had taken much of the property and want to sell the antiques back to the government. For example: Queen Sheba's throne. If the government tries to take the stuff back, the locals break it.
Aksum needs more funding for it to compete with the major sites in Egypt and Morocco. It has a lot to offer for allocentric tourists, but I was a bit disappointed.