Your "Lilliputians" are the size of dust mites. They will be barely visible on a human being. This answer will assume they are sapient and have technological civilization. Their amphibian spaceship is evidence of these facts. It will not assume they are humanoid or anything close to humanoid. They are alien creatures the size of dust mites.
The fact they are seeking a human body to colonize is an indicator that on their home planet there are large animals that act as hosts to their parasitic civilization.
The most likely site for their colonization and settlement will be on the skin of their human host. Areas of the human anatomy covered by hair will be the most probable sites. The top of the head and the pubis. This is airy, this means oxygen will eb accessible and available, not too humid or too hot, and an excellent location for solar power collectors. Any solar energy technology will be far advanced beyond what we have currently developed. If they have space travel, their solar energy technology will be comparably more advanced.
Food. That be will be gathered from oils, skin fragments and the bacteria that colonize the human epidermis. If necessary they could drill into the skin and extract nutrients from the interior of the human host.
Many mites are parasitic on plants and animals. One family of mites, Pyroglyphidae, or nest mites, live primarily in the nests of birds and animals. These mites are largely parasitic and consume blood, skin and keratin. Dust mites, which feed mostly on dead skin and hair shed from humans instead of consuming them from the organism directly, evolved from these parasitic ancestors.
Source: Parasitism in mites
This generally assumes the "Lilliputians" are functionally mites as we know them on planet Earth. Whatever structures they set up on their host will depend on a more detailed knowledge of their biology, anatomy, reproduction, and ecology. To say nothing of their culture and social organization.
Also, we will need to be careful about how they use their advanced technology. Having amphibian spaceships blasting off and landing on the head of their human hosts might bring unwanted attention to their presence. Humans have developed a considerable measures for removing ectoparasites like lice from their bodies. The "Lilliputians" may need to be discreet with their technology.
In conclusion, the head and pubis seem to be the most probable sites for "Lilliputian" settlement on a human host. With the head offering the most benefits.