Dubai is a city of wonders. Everything there is must visit ones. But to mention few i shall list following
1) Burj Khalifa (Tallest building in world)
2)Burj Al Arab (only seven star hotel in the world) (not only) i think first 7 star.but we need to buy a ticket for entry. :huh
3)Dubai Mall (Largest Mall in the world)
4) Dubai Metro (Longest driverless fully automated metro in the world).. I am proud to be a part of the team who built it
5)Palm jumeira islands (Man made islands)
6) Atlantis hotel and its Aquariums
7) Jumeira beach
8) Miracle gardens
9) Desert safari and belly dance
10) Souqs in Deira and Mina Bazar
11) City Centre
and countless number of wonders..
Regarding shopping you can buy gadgets like mobiles,game consoles etc for cheaper than india
LED and LCD TVs are also cheaper but taking it to india will force to shed some more money as customs duty..
And at last not but least petrol it is very much cheaper than India but you cant take it to india just kidding