This is the capital of Rhode Island and one of the oldest cities in the United States. It has lively dining, arts and theater scenes. Low-cost events and attractions are available throughout the city. For instance, the RISD Museum is free every third Thursday from 5 to 9 p.m. and Sundays from 10 a.m. to 5 p.m.; and admission to the Botanical Center at Roger Williams Park only costs $5 for adults and $2 for children.