Some primary sources available in print form at the Duggan Library:

Eliza Farnham, Life in Prairie Land (1846) – Illinois in its frontier era.
Sandra L. Myres, Ho for California! (1980) – an anthology of women's diaries.
Eliza Flower, Letters of an English Gentlewoman: Life on the Indiana-Illinois Frontier, 1817-1861 (1991).
Barbara Lawrence and Nedra Branz, ed., The Flagg correspondence: Selected Letters, 1816-1854 (1986) – Illinois in its frontier era.
Rebecca Burlend, A True Picture of Emigration (1936) – an Englishwoman settles in Illinois during its frontier era.

Some primary sources available online:

Sarah Bixby-Smith, Adobe Days (California in the 1850s)
Julia Louisa Lovejoy, letters from Kansas, 1855-1863
Catherine Sager Pringle, Across the Plains in 1844
Mattie Oblinger, letters and photographs (Nebraska in the 1870s)
Narcissa Whitman, letters and journals, 1836-1847 (Oregon)
Luzena Wilson, memoirs of the Gold Rush in California


Any of these sources can lead you to other interesting items. Check with me or any of the reference librarians if you need help finding sources or confirming that they were written during the time under discussion.