By definition, the targets of nativists are immigrants. Nativists are people who believe that the natives of their country are superior to immigrants. They tend to believe that the immigrants are a bad influence on the society of their country.
Over the years in the United States, nativists have had different targets as immigrants have come from different places. The first major wave of nativism was in the 1850s when the Know-Nothings arose. This nativist group was largely opposed to Irish people as well as other Catholic immigrants. By the 1880s, nativism, especially on the West Coast, was generally directed at Chinese. This led to the Chinese Exclusion Act of 1882. Later on, in the 1920s, there was nativism that was directed largely at immigrants from Eastern Europe and Southern Europe. This led to immigration restriction laws in that decade. Today, we still have some degree of nativism. Today, nativist attitudes are generally directed against Hispanic immigrants.
All nativism, then, is aimed at whatever group of immigrants is most numerous at a given time. It is typically driven by worries that immigrants are taking Americans’ jobs and/or diluting their societal and cultural values.