Yes, of course you can combine
Fujairah & Dubai vacation during your stay at Fujairah. It's very close to
Dubai, so you can well enjoy and explore Dubai within easy reach, but first stay at Fujairah and explore the place for 4 days then travel to Dubai by car, it's just 132kms from Fujairah and there are many comfortable
transportation available, bus and car. if you would like to go by car then you will reach within 2 hours. The bus service is also inexpensive, so choose whatever you want.
Fujairah is a wonderful place to visit and stay. It has many
attractions including historical places and beaches, enjoy this place and go to Dubai and stay there for 7 days, Dubai has also many
things to do, so explore all the places of Dubai. Visit
Dubai hotels page to get accommodation information.
Hop you will enjoy both the emirates with more fun!