Dubai

https://images.sunshine.co.uk/ss/maps/113/0/2835/9756_10.pngCruise ships dock at Port Rashid.
Three large modern cruise terminals next to each other offer their services.

Though the cruise terminals looks quite close to the city on a map, it's  located in the centre of a cargo shipping port, so you will not be able to walk to see the sights in Dubai.  You will need to take the shuttle or taxi.  Some malls may offer free shuttles and have desks set up inside the terminal with their schedules posted. Shuttles typically run from 9:30am (malls open at 10am) until 5 to 7pm. Malls running shuttles are Mercato, Wafi, Dubai Outlet and Bur Juman. Or by taxi.  Since there is a surcharge for taking a taxi from the port, it will be cheaper to take a shuttle first to the mall closest to your destination.

Here are some videos from Dubai
Dubai Mal and City tour
Abra Tour Across Dubai Creek
Dubai old Souks

Hop on/off buses will be at each terminal, transporting you to a point where the red and blue lines meet. (Wafi Mall) Here you can take an hop on/off bus. This bus will also take you back to the port.

Inspirations for walking tours in old Dubai:
Old Dubai do-it-yourself walk
National Geographic:
Dubai Walking Tour: Old Deira
Dubai Walking Tour: Dubai Creek and Shindagha
Dubai Walking Tour: Bastakiya

Sights

  • Deira Souks, Visit the Gold Souk, and to the close neighbours follow your nose to the Spice Souk and the Perfume Souk. Across the Dubai Creek, wander through the Textile Souk in Bur Dubai and dig through swaths of brightly coloured silks and embroidered fabrics.  Link here
  • Bur Dubai , the oldest part of Dubai, on the south side of Dubai Creek is home to many historic sites, museums and old buildings. Tour the living museums of the Heritage and Diving Village in Al Shindagha and explore the souks. Or wander through the lanes of the historic Al Fahidi Historical Neighbourhood, home to some of the only original Arabic wind-tower houses left on the Arab side of the Gulf, built by wealthy traders and pearl merchants. 
  • Burj Al Arab Hotel - This sail shaped hotel is an iconic image of Dubai. There is heavy security at the gate so the hotel can be best admired from Jumeira Beach nearby. Take a taxi from Mall of Emirates metro.
  • Burj Khalifa - Recently taking the crown of tallest building in the world, there is an observation deck midway up with an outdoor platform. Enter from Dubai Mall. Tickets are much cheaper if you reserve but you can do it for the same day if it isn't busy. 100 AED for timed entry. http://www.burjkhalifa.ae Update Oct 2014 - A new observation deck has opened higher up on the 148th floor, 24 floors higher up than the current observation deck.
  • Dubai Mall - The largest mall in the world with an indoor theme park, multistory aquarium and skating rink. Catch the fountain show outside every half hour from 6pm to 11pm. Metro Burj Khalifa/Dubai Mall. Metro Link, an air conditioned, moving walkway opened Dec 2012 easing the connection from the mall to the metro station.
  • Ski Dubai - The largest indoor ski slope inside the busy Mall of Emirates. Entry includes rental of winter clothing and ski equipment but you but need to purchase gloves and a hat. Bring your own to save some money if you plan to visit. Metro Mall of Emirates. http://www.skidxb.com/
  • Palm Island - This manmade island features an Atlantis resort at the very top with a water park and aquarium. A monorail runs along the center of the island.
  • Dubai Museum - This museum showcases Dubai's history. From the museum, head over to the Grand Mosque next door and take an abra across Dubai Creek to visit the Deira district with the Gold and Spice Souks.
Shopping
  • Dubai has many modern air conditioned malls with the most popular ones being Dubai Mall and Mall of Emirates. Popular NYC burger and shake restaurant Shake Shack can be found in Mall of Emirates. Malls typically open daily from 10am to 10pm or midnight.
  • Gold Souk - an outdoor historic market in the old city center, Deira district. Official hours 7am-noon & 5pm-7pm Sa-Th, 5pm-7pm Fr, closed Sun but most shops remain open in the afternoon. There are also modern gold souks in Dubai Mall and Wafi Mall.
  • Spice Souk - south of the Gold Souk and specializing in spices, Deira district
  • Souk Al Bahar - a modern souk located beside the Dubai Mall across the walkway over the fountain
  • Dubai Marina - Skyscrapers surround this modern marina with plenty of restaurants and shops and a beach. The Jumeriah Beach Residence (JBR) Walk is in the area. Located by the base of the Palm. Metro Dubai Marina.
  • For supermarkets, look for the large French chain Carrefour in the malls (Mall of Emirates and Wafi). Dubai Mall has a Waitrose supermarket. Carrefour opened in 2014 inside Burjuman Mall and there is also a Spinneys about 2 blocks to the south.
Internet
Free wifi is available at Starbucks and other cafes, inside Dubai Mall, and in the cruise terminals (difficult to connect when busy). There are also free internet computers in the terminal. 

Dubai History
Dubai is the most famous of the seven Emirates in the United Arab Emirates (UAE).
The story of ‘modern’ Dubai is  short. The Emirate has been established for thousands of years, yet within the last few decades, Dubai has transformed itself into the ambitious, dynamic Emirate as we know today.
In 1894, the introduction of full tax exemption invited traders around the world to take advantage of the Emirate’s unique benefits. In the 1940’s and 50’s, Dubai prospered in the gold trade, providing a strong economy for its 40,000 population. This was just the start as the mid 1960’s unveiled the discovery of oil and Dubai’s economy went into overdrive, leading to an influx of foreign workers.
In 1973, Dubai joined the other Emirates to adopt a single, uniform currency: the UAE dirham. In the late 70s, the Jebel Ali Free Zone was created, comprising the world’s largest port and providing foreign countries and businesses unrestricted import and export. Today the population is 2,7 million.