Love this part of the world.
If you're wanting the traditional afternoon tea experience then the Burj Al Arab in Dubai or Emirates Palace in Abu Dhabi are both excellent.
As mentioned above, the Grand Mosque in Abu Dhabi is also a must visit.
I'm a big fan of Muscat too - the souks have a biblical feel and some of the desert scenery is stunning. You'll be hassled a little bit when you exit the port by vendors wanting to take you on a tour, but just be firm and its fine once you're a little further down the promenade.
Not sure what Level 3 means but you'll be extremely safe in the UAE. Dubai is safer than London/Paris/New York, much cleaner and you'll receive far better level of service.