what is the origin of the state's name where the city is situated?
It is unclear how the island came to be named "Rhode Island" but "Providence Plantation" was the name of the colony founded by Roger Williams in the state's capital of Providence
Rhode Island
 "Providence Plantation" was the name of the colony founded by Roger Williams in the state's capital of Providence. This was adjoined by the settlement of Warwick; hence the plural Providence Plantations.

It is unclear how the island came to be named "Rhode Island", 
for what is "providence, rhode island" famous? Providence is the capital and most populous city of the state of Rhode Island and is one of the oldest cities in the United States what kind of culture is followed over there? It has a non-rhotic accent, has most coffee and doughnut shops and restaurants per capita of any city in the country and in reputed as one of the most active and growing gay and lesbian communities in the Northeast are there any sister cities to it? Yes. It had five sister cities mention a few interesting sites over there? Waterplace Park and Riverwalk, Roger Williams Park, Roger Williams National Memorial and Prospect Terrace Park why is the last site interesting? For its dramatic elevated view of Providence's "downcity." when was it opened? 1869
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Rhode Island [SEP] Origin of the name
The name was officially applied to the island in 1644 with these words: "Aquethneck shall be henceforth called the Isle of Rodes or Rhode-Island." The name "Isle of Rodes" is used in a legal document as late as 1646. Dutch maps as early as 1659 call the island "Red Island" ("Roodt Eylant").