How do tourists make their tourism choices and what are the factors that influence those choices?

First, different types of tourists are influenced by different factors. A well-educated elderly couple spending a summer traveling around Europe may have very different motivations than a college student on spring break in Florida. People with young children will obviously prioritize locations that have activities and facilities geared towards family travel, while the elderly or disabled may be concerned about accessibility.
The single most important factor influencing destination choice is recommendations from friends or family. This effect is amplified by social media, on which people often share vacation photographs and anecdotes.
Price is an important factor, too, with sales or special offers sometimes motivating people considering a specific destination to decide to visit it; someone who is reluctant to visit a given hotel at $250/night might decide a $150/night special makes that hotel affordable. 
Often, people enjoy visiting places they have seen or read about, with Jane Austen fans deciding to visit Brighton or people who enjoyed the Lord of the Rings films visiting New Zealand to see the stunning scenery they enjoyed in the film. History enthusiasts will visit scenes of famous battles or other historical events, while on a more poignant note, Jews might visit the remains of Nazi concentration camps or Holocaust memorials, and many relatives of fallen soldiers or civilians may visit war memorials or the 9/11 memorial as part of exploring their own roots.