Travelled to Hong Kong, Thailand, Toronto, Niagara Falls...all before DD hit two years old. Mind you, these destinations were spaced out over three separate trips.
I second the poster who touted baby-wearing - DD's baby carrier (or as my DH calls it, the "baby back knapsack") was a lifesaver and allowed us to basically take her anywhere.
At one, DD loved water, so she really enjoyed the pool at the hotel, and the beach. She also enjoyed the butterfly conservatory at Niagara Falls, and all the flowers.
Like many other posters, I would recommend renting somewhere that has laundry and kitchen facilities. That way, you don't have to pack as much clothing.
Honestly, at one years old, DD didn't much care about the sites. As long as she had her mummy, daddy, and security blanket, as well as a couple toys, or grass to look at, or leaves to pull off bushes, and as long as she was kept on her regular schedule, she was happy.