1850 Fed Census NY, NYC, Ward 10, p 38 (handwritten), dwelling 529, family 1257 (ancestry.com)
John R Baxter, age 21, clerk, b NY
Mary Baxter, age 19, ---, b NY
Eliza Pitts, age 38, ---, b NJ
Eliza Randle, age 63, ---, b NJ
Perhaps Eliza Randle is an aunt? Something to look at.