As Dubai is only few hours away from Muscat, it's not hard to go there for a long week-end if you get bored with Oman. You will need between 4 and 6 hours to reach Dubai from Muscat by car : it depends on how fast you're driving, the traffic jams and the time you'll spent at the border post (If you have a Omani hire car, you will need also to get a 12 OMR insurance policy extension at your rental agency).
Dubai is so different from Oman : you have a lot of towers, it is a crowded city with traffic jams and you have a lot of activities to do in the city ! You can check the Sheikh Zayed road with its hundred of towers (including the Burj Dubai, the tallest tower in the world), you can go to the Burj Al Arab and the Jumeirah beaches, you can also visit some old typical houses in Bur Dubai (even if they look as new as the towers because of their recent renovation)...
There a lot of Souqs as well, and a interesting Dubai museum. Also you can make some skiing in the Mall of Emirates (which is a change from the heat of the city !) or spend the day in the water amusement park "wild wadi".
In brief, I've spent 3 days in Dubai during the Eid holidays and it has been a real enjoyment and a big change from Muscat. However, more than 3 days I don't know what I could have done more (maybe more shopping ?).