Punta Carna in the Dominican Republic has a beautiful looking terminal with a thatched roof of all things, but to answer the original question "can an airport be functional and look good?" It would seem not. Last time there we had to queue for an eternity both in and out to give some grumpy old duffer $10.
At least it looks better than Barbados which earlier posters have mentioned and where you will also queue for more than an hour for the pleasure of being welcomed to the island.
