While the Indian Ocean is enticingly close, some parts of the beach would not seem to be a good option to swim at. However, the city of Diba which is 30km far from Fujairah city would be a good choice, where you can enjoy the sunny beaches and you can practice any sea activity you like. One more interesting thing to do is that you can make a boat trip to one of many islands that lie in the Gulf of Oman, a really wonderful places to visit and it is a good place for fishing.
All things considered, Fujairah is probably more suited as a base from which to go on excursions to the surrounding areas most of which are enclaves of Sharjah, rather than doing anything much else. The city is growing in stature as a business destination, particularly where oil is concerned, but tourism remains somehow significantly behind.