In the first half of Gulliver's Travels, where is there an example of Gulliver being curious?
Gulliver, through intention or misfortune, constantly finds himself in strange places, surrounded by strange people. Because of this, he always has to figure out his environment and the culture to avoid giving offense. Examples of Gulliver's innate curiosity appear all over the book, and he compiles and lists (to a somewhat obsessive level) the customs, measurements, and other interesting facets of each culture. For example, while he is acclimating in Lilliput, Gulliver compiles a list of culture and custom even larger than what is set forth in the novel itself:
Although I intend to leave the description of this empire to a particular treatise, yet, in the mean time, I am content to gratify the curious reader with some general ideas. As the common size of the natives is somewhat under six inches high, so there is an exact proportion in all other animals, as well as plants and trees...
(Swift, Gulliver's Travels, gutenberg.org)
He makes claim several times to even more information, which he intends to publish as a scholarly text. This indicates his drive to learn and study, and his need to discover and collect information and data about his surroundings. Each time Gulliver lands on a new shore, he despairs of ever returning to England, but each time he carefully assembles a mass of information, indicating that even if Gulliver were to remain in one of those countries until his death, he would spend his remaining days asking questions and collecting facts, figures, and information.