The oldest building in Abu Dhabi is from the 19th century, and the city has, in other words, not much to offer those interested in history. The building mentioned is known as the Al-Husn Palace and was built on top of the city's water supply.
A pleasant, although not very comprehensive, pause from the skyscrapers is the fish market Dhow Wharf, and if you're there early enough, you'll see the fishermen bring in their catch.
This fort, which later became the headquarters of both the emirs and the government, and is now the city museum, was erected at the beginning of the 19th century. The building is probably the oldest in Dubai, and the exhibitions tell the history of Dubai in pictures and accessories, just as you can also gain insight in the Emirate's and the city's geography and nature. You can also gain insight into the many archaeological excavations in the area.
The most interesting attraction is a sail on the river where you can hire a so-called "Abra" for an hour or a half -remember to bargain about the price - and sit back and relax. Let then the captain navigate you through the many ships and boats from all over the world, loading and unloading at Dubai harbour.
If you want to see the desert in the Emirates, Dubai is the best point of departure. Several tour organizers arrange both short and longer trips, including dune driving, sand skiing, animal watching and the mandatory camel ride and a lot more. In fact, great initiative is shown in the effort of making the desert a fantastic experience for tourists.
The only sight in Fujairah, besides the beaches, is the archaeological and ethnographic museum. It has a fine collection of finds from local excavations, and the ethnographic section contains weapon, household objects and dresses from Fujairah's history.
An interesting peek into the Emirate's ancient handicraft traditions is offered at the women's craft centre, Handicraft Industrial Center, in the capital city of Abu Dhabi. The women here keep a number of handicrafts alive and the products displayed are naturally for sale. You should be prudent, though, as some of the women don't like the presence of men at the Center.
From the 37th floor in the World Trade Center, you'll get an excellent view of the impressive city that Dubai in fact is, and you can get in as a part of the organised tours which are arranged daily.