Neighbouring Sharjah, while dry no alcohol and mostly suburban, has a few beaches and museums of interest.
The capital of the United Arab Emirates, Abu Dhabi, is an entirely different city and it is worth the one and a half hour ride to see the contrast.
The city of Al Ain located near to the borders with Oman is surprisingly a city of lush gardens and trees - an aspect quite unusual in this part of the land considering its desert surroundings.
Visit the peaceful Umm Al Quwain emirate if you want a cosy and relaxing environment, free from city hustle and bustle.
Dubai has an arrangement with Oman to allow visitors who qualify for an Omani visa on arrival by road through Hatta.
The Iranian island of Kish is close by, and is an economic free-zone that does not require a visa.