I get asked all the time about the best things for visitors to do in Dubai, so I'm putting my thoughts down for easy reference! Here's my list:
New Dubai/Downtown Dubai/Dubai Mall area: the Dubai Mall is where you'll find the best high-end shopping, a full-size skating rink, the Dubai Aquarium, and the entrance to At the Top of Burj Khalifa (the world's tallest building). You can buy timed tickets in advance for 125 AED or pay 400 AED for immediate entry to the observation deck of the Burj Khalifa ((http://www.burjkhalifa.ae/en/ObservationDeck/TicketInformation.aspx). Walk across the bridge over the fountain area to see the Souk Al Bahar (many small gift shops and nice restaurants--Rivington's balcony has a great view of Fountain show) and the Palace Hotel (Asado's Argentine steak restaurant)
Dubai International Financial Centre (DIFC): (where many business offices are located) is a short drive from the Dubai Mall with many offbeat art galleries and restaurants. Especially good are Zuma, La Petite Maison and Ivy
Jumeirah Mosque: tours are offered at 10 am every day except Friday, arrive at 9:45, no reservation needed, 75 minutes long (http://www.cultures.ae/index.php/ouractivities/jumeirah-mosque-visit), have lunch afterwards at Lime Tree Cafe nearby, cross Jumeirah Beach Road and take a walk on the beach
Old Dubai: Dubai Museum in Bur Dubai (open every day from 8:30 am-7:30 pm except Friday opens at 1:30 pm); stop in the XVA Art Hotel/Gallery nearby with nice restaurant and gift shop; visit old souks--textile souk is on the Bur Dubai side where the museum is, take an abra to cross the creek and visit the gold and spice souks on the Deira side of the creek. Stop in the Sheikh Mohammed Centre for Cultural Understanding, which offers cultural meals (breakfast and lunch) and heritage tours (http://www.cultures.ae/index.php/ouractivities)
Jewelry: try the Gold & Diamond Park at Interchange 4, Sheik Zayed Road; Mamiya's shop is recommended for Arabic influenced pieces, cheaper than gold souk
Desert Safari: many of these involve "dune bashing", which is not recommended if easily nauseated--look for a different type of tour, maybe in early morning or evening. Check out Platinum Heritage safaris--breakfast with a bedouin and falconry and wildlife offerings sound interesting (http://www.platinum-heritage.com/heritage-collection). Consider visiting Bab Al Shams--classic desert resort, good place to start desert excursion
Jebel Ali Shooting Club: skeet, trap, sporting clays, pistol range and archery
Mushrif Park: desert hack on horseback at the equestrian club, nice track for running and biking (bring your own)
Other malls: Mall of the Emirates (Ski Dubai), Mercato (small, on Jumeirah Beach Road with new movie theatre)
Unique restaurants: Bu Qtair fish shack in Jumeirah, Ravi's in Satwa, Antique Bazaar (Indian with alcohol and live entertainment) at Four Points Sheraton Bur Dubai. Decent restaurants close to our apartment in Jumeirah 3: Arz Lebanon, Reem al Bawadi, Barracuda, Smiling BKK, Jones the Grocer, Marita Bonita, Shakespeare & Co., Rock ‘n Sole Plaice
Seawings flight: (http://www.seawings.ae/scenic-tour/dubai/) leaving from Jebel Ali Hotel: aerial tour of Dubai, expensive, highly recommended, and by far the best way to see the man-made islands, which do not look like islands from the road level
Global Village: amusement park with booths from countries around the world selling arts, crafts, clothes, and foods, very cheap, opens late afternoon winter season only so check before going
Palm Jumeirah: Atlantis Aquaventure and Rostang, the Italian restaurant at Atlantis; Jumeirah Zabeel Saray (Turkish theme luxury hotel), especially the coffee bar and Voi, the Vietnamese restaurant; 101 restaurant at the One and Only the Palm
Madinat Jumeirah: nice shops and theatre near Burj Al Arab, favorite restaurants include Anar (Persian), Pierchic (most scenic) and Friday brunch at Al Qsar (highly recommended)
Camel Racing: the new camel racetrack is in Al Marmoum--take the Al Lisali exit off E66 (the road to Al Ain) before Rugby Sevens stadium--winter season only--races at 7 am and 2 pm. Call to confirm race days and times before heading out--Dubai Camel Racing Club (04 832 6526). Admission is free, very few spectators, mostly locals.
Timeout Dubai: the weekly magazine and website (http://www.timeoutdubai.com) are a good source of information about local events and special offers. Meal deals, special offers and coupons are very popular and widely used by expats in Dubai to counter high prices.
Further afield, a few must-sees:
Abu Dhabi: the Grand Mosque, tours daily except Friday, Palace Hotel, Corniche
Al Ain: Jebel Hafeet mountain (good lunch at hotel at top), Wildlife Park, Palace Museum (former home of Sheikh Zayed, UAE's founder), National Museum, Oasis
Doha, Qatar: Museum of Islamic Art, designed by I.M. Pei; Damien Hirst's new series of monumental sculptures outside Sidra Medical and Research Center; the "Relics" retrospective of Hirst works at Al Riwaq (may be fully booked through November)
