I would absolutely recommend these attractions when you visit Dubai.
1. Mall of the Emirates: The largest shopping mall in the Middle East, housing the Middle East's first indoor ski slope, measuring 400 meters and using 6000 tons of snow. The mall is home to over 450 international retail brands.
2. Burj Dubai: This will be the world's tallest building, although a hotel, this is one of Dubai's major tourist sights.
3. Dubai Museum: Believed to be Dubai's oldest building. Built in 1787, the Al-Fahidi Fort houses the Dubai Museum. The Museum offers a unique trip to desert life, traditional Arabian homes, mosques, fishing, pearl diving and trade. Major highlights of Dubai Museum are artifacts from excavated graves, musical instruments. Deadly weapons also form the major part of Dubai Museum, such as swords, spears.
4.Gold Souk: The Gold Souk is Dubai’s most famous market. Explore the alleyways and narrow streets that are lined with shops bursting with gold necklaces, brooches, rings, bangles and earrings. Be dazzled by a staggering display of gold, and more gold!
5. Sheikh Saeed Al-Maktoum House: Built in 1896, Sheikh Saeed Al-Maktoum House, Dubai is an iconic structure from the olden days of Dubai. Saeed Al-Maktoum was the brain behind Dubai Creek, one of the magnificent marine attractions for the tourist’s world over. This erstwhile ancestral home for the Al-Maktoum family for several generations has witnessed several watersheds in the History of Dubai.
6. Desert Safari Dubai: A drive through the desert dunes is unparalleled, if you are the adventurous sorts. You come across camel farms, and delicious barbecue joints where you could also take in the Shisha, the famous Arabic water pipe, with varied fruity flavours of peach, strawberry and more.
7. Ibn Battuta Mall: The Ibn Battuta Mall is a large shopping mall themed around the journeys of the traveler and explorer Ibn Battuta. The mall is divided into six courts each based on the areas he visited on his travels: China, India, Egypt, Tunisia, Persia and Andalusia; each court is decorated to resemble each of these areas of the world.
8. Jumeirah Mosque: Normally no one who is not Muslim is allowed in any mosque but the Jumeirah Mosque is the only mosque that is open for non-Muslim visitors. Take a tour guide to understand the Muslim culture, traditions, and religion.
9. Seawings Dubai: Take this amazing seaplane ride and see the amazing sights of Dubai from the sky - The Palm, The World, Burj Al Arab, The Burj Dubai, Dubai Creek and more. It gives you a whole new perspective of Dubai.
10. Dubai Creek - This is one very enjoyable experience, especially when you get a boat for you and your partner, or family, and tell the driver to take you for a very nice ride, which eventually ends up on the other side the creek.
With a little bit of research you could be staying right near all of these attractions. To book into a mid-priced and comfortable hotel you could opt for the Citymax Hotels. They are coming up with 3 major hotels for the budget traveler. Each of these hotels are located near at least 3 or more important historic places either in Dubai or Sharjah.