Jumeirah Mosque is one of Dubai’s main attractions for good reason: it’s the only mosque in the city that is open to non-Muslims. Guided tours are organized daily (except Fridays) at 10.00 and 14.00. You should be there half an hour before to make sure you get a seat. The tour lasts about 1h15.
You will of course need to be properly dressed: Arms and legs must be covered (that applies to everyone), and women should cover their hair as well. You can visit the inside of the mosque and learn more about the rites and the 5 pillars of Islam. Photos are allowed.