The answer is not very big!
The area of American Samoa is 199 square kilometers (77 square miles), spread over seven islands in the mid-south of the Pacific Ocean.
To put this into perspective, The Maldives, the smallest country in Asia, has an area of 300 sq km (120 sq miles), while St Kitts & Nevis, the smallest nation in the western hemisphere, is 261 sq km in areas (101 sq miles).
Were it a sovereign state (rather than an unincorporated territory of the USA), it would rate larger than some of the European micro-states, such as Liechtenstein (160 sq km, 62 sq miles).
To compare all this with one of the largest US cities, the land area of the city of Chicago is 588 sq km (234 sq miles).
The largest island in the American Samoa chain is Tutuila, at 142.3 sq km (54.9 sq miles). The island of Tau, the largest of the three island Manua zone, is 44 sq km in size (17 sq miles). The smallest islands are Rose Atoll (5 sq km) and Swains Island (1.5 sq km).
This YouTube user took a drive around American Samoa's main island, and should give you a sense of scale: