Give me some suggestions of things not to be missed!

DH and I booked our trip yesterday! We'll be headed to Korea to visit my friend from high school, but first we'll spend 3 days in Dubai.

In Dubai, I know there's shopping obviously, but not sure what else to do? I'm totally fine with just sitting by the pool or at the beach all day! But if there's anything we just "have" to do, let me know! We'll only be there for 3 days. Also, when not at the resort, how to dress? Is it a Muslim country? I want to be respectful.

Then in Korea: We'll go to Jeju Island for a few days. DH says we must go to a BBQ place, but since I'm a vegetarian, that doesn't excite me much! lol So...what to do? I'm sure my friend will have lots of ideas, but I just want to hear what you think? I think there is a Hello Kitty Cafe there?! I def. would wanna check that out lol

I'm so excited for this trip! After the disappointing year we've had TTC and recent MC, and with how busy I've been with my business, I think I really deserve it! :oD

So hit me with some fun suggestions, if you have 'em!