We got this incredible new travel high chair that we bought before our vacation. It is a lifesaver! You just blow up the seat, attach the straps in all 4 directions around the seat and back of the chair and then strap in the baby! It takes up no space compared to every other one I've seen. Ours is a French model (Bea.ba), but I know I've seen them in the States (from Fir.st Yea.rs). I would recommend it!
One caution... Love Bug figured out how to push herself back and luckily we saw this before the chair fell over. So we just learned to push her away from the table or turn her sideways. If we were at a restaurant and had no room to do either of those, we put or feet on the bar of the chair, just below the seat. It's a small safely concern compared to the seats that attach on the table. Everyone seems to have horror stories of one falling with a child in it.
Our trip really wasn't that bad... we couldn't lay on the beaches, but they were beautiful and we just enjoyed relaxing as a family.