For me it's a combination of many things and depends on the time we have available.
I'm a history buff so like to check out historical monuments, museums and listening to locals stories.
But as you would have seen from previous sites I also like food. I haven't yet made a decision on where to travel based on what will be available to eat (because I will try almost anything once), but I defiantly will seek out the local cuisine, such as Chili Crab in Singapore or that unusual restaurant, like the place - M Restaurant - in Budapest that was covered in brown paper.
M Restaurant Budapest
I'm big on the great outdoors, so National Parks are high on my list, like Kings Canyon National Park in California. But recently so is hiking like the Bay of Fires in Tasmania. We actually have a dream trip that picks off a number of National parks on the west side of the USA we hope to do someday.
Plitvice Lake, Croatia
We like to try and keep things "sustainable" when we travel to locations, particularly those in the third world or developing countries. Sustainable means different things to different people, but for us it's trying to stay local (although we will stay in the Hilton on an odd occasion!), eating local produce (like eating at Friends in Cambodia) in locally owned restaurants and trying to make sure that basic human requirements are met, such as porters rights on the Inca Trail. This is one can be difficult to implement depending on what it means to you.
Staying local in Mauke
Eating at a local Yum Cha place in Hong Kong
On different trips this will mean different things. Sometimes it can be that you get your own bathroom (no communal showers!), other times it can be that your relatively isolated with good food like our trip to Wilson Island. It's not a key criteria, but we always try to do one thing that has a high level of comfort.
The Hilton Moorea (breaking the keeping it local style above)
For DH it's all about can he squeeze in another AllBlacks game.
What's your travel style?