I travel a lot with my pump and have even been to countries such as Mexico and the Philippines where the pump is not as common. I haven't had any problems with it yet, but I always carry a note from my doctor that says it is a medical necessity, although no one has ever asked to see the note thus far.
I have gone to water parks, beaches, cruises, and snorkeling w/my pump. I have a waterproof sport case for my pump that allows me to stay attached while in the water. A lot of times, I will disconnect my pump while participating in water activities though and just make sure I have some kind of waterproof cooler to keep my pump dry and out of the sun. However, I don't think that as diabetics we are allowed to go scuba diving. It's not because they are discriminating against us, it's more of a health precautionary. If we have a low while scuba diving, we may not be able to surface fast and safely enough to get the treatment we need to correct it, so they would rather not chance it, that sort of thing.
The disadvantage about traveling with a pump is that sometimes it may take you a little longer to go through security, especially in airports that are not as experienced with insulin pumps. I have been able to pass through security without being "frisked", but I have also had to go through security with a full pat-down and swabbing.
As for wearing clothes, it can be challenging if you don't have pockets, but yes, I have clipped my pump on to the front of my bra just between my cleavage and have been able to wear form fitted dresses that way. There are also accessories like arm/leg bands that velcro around your arm or leg and have a pocket attached to it so you can slide your pump into it and hide it under your clothes. Or you can make your own little pocket for your pump and then attach it inside your clothes with a safety pin.