Weather in Jan is good..
You will also get dubai shopping festival in full flow.
Tickets are not cheap plus hotel rents will also be on the high side. but its nearer than the other 2 places you mentioned..
Places to see are many and a good time and money well spent
BUT i would suggest you go for Malaysia..
Get a booking done thru emirates. Book a flight from A-380 Super Airbus. Enjoy the 7hr ride from dubai to Kuala lumpur. KUL is a brilliant place to visit plus the ideal vacation getaway island.
Plus when you go with emirates ask them to arrange a transit visa to dubai while coming back. so you can see both places.
Expense will be almost the same.. what you save in airfare to dubai from kul. you will spent it in hotel fare and transportation.
Rest istafaa knows better..
good luck