When I was in The UAE 5 years ago with my family and a friend, we took a trip right to the UAE/Oman border to the city of Al Ain. We went from there to the Oman side to a city I can't remember the name of and we went to a camel market, old fort/museum, and a traditional market (where a guy tried to sell me an AK
-47 for USD $200). It was a very eye opening experience to see that kind of poverty all around but it was totally safe as there were quite a few buses carrying European tourists (mostly Russian and German). You can easily make the Dubai-Al Ain/Oman round trip in a day.
"Drunk drivers run stop signs. Stoners wait for them to turn green."