If you are an adult and know your perscription ( you can get one from Moorfields eye hospital Dubai) then you can order online from abroad, we buy all our glasses from the UK for a much better price they are delivered very quickly.
We have used eyewearbrands.com with good results.
If you just need new lenses, I went to Yateem for a new prescription very recently, and it cost 250dhs for the testing and lenses (really just the lenses though, the testing was free of charge). Got my glasses returned to me within 48 hours. I'm not sure how that stacks up against other opticians (I went there because of convenience) but at least you can call some other opticians and see how the price compares.
I'm not sure where to suggest for frames, sorry. I knew exactly which frames I wanted and didn't really browse around.