1840 census for Waterbury lists Nathan Hill. Other info illegible.

1850 census for Waterbury p. 609 lists Nathan Hill age 46 born N.H., Lucy age 44, Isaac N. age 19 born Vt, Sarah P. age 17, Lydia A. age 14, Elizabeth C. age 12, Julia T. age 9, Juliann M. age 6.

1860 census for Waterbury p. 137 household 1310 lists Nathan Hill age 56 born N.H., Lucy age 54 born Vt., Sarah age 27, Julius age 19, Delia M. age 16. (On p. 141 household 1368 is "Lavila" Brown, age 35, his future 2nd wife).

1870 census for Waterbury lists Nathan Hill age 65 born N.H., Survilla age 45 born Vt.

1880 census for Waterbury lists Nathan Hill age 76, wife Survilla age 55 (no birthplaces).

Waterbury, Washington County, Vermont, Land Records: Vol. 25, 1882-1889 P. 11: Nathan Hill and Survila his wife on Nov 29 1880 sold to Cyrus Fisk their "farm where we now reside" in Waterbury, originally purchased in March 1864 from Lewis J. White and Lydia A. White recorded in Book 18 page (unreadable). (Source: FamilySearchLabs.org Vermont Land Records > Waterbury, Washington). [Note: Lydia A. White was their daughter.]

An 1873 map of Waterbury, VT, shows the location of the "N. Hill" residence in District No. 6.
http://content.ancestry.com/Browse/view.aspx?dbid=1205&iid=USAOTH2007MAP_145105-00029
Buried in Old Waterbury Center Cemetery, Waterbury, Vermont:
Demeritt, R. W.; 1836--1918
Hill, Sarah; his wife, 1833--1897
...
Hill, Lucy; wife of Nathan Hill, d. Sept. 18, 1861 AE 55 yrs
Hill, Isaac N; son of Nathan & Lucy Hill, d. Sept. 2, 1854 AE 22 yrs 7 mo
Hill, Delia M.; dau of Nathan & Lucy Hill, d. Dec. 15, 1861 AE 17 yrs 9 mo
1 small blank marker
...
Sleeper, David D.; d. Mar. 3, 1892 AE 58 yrs
Sleeper, Elizabeth C.; his wife, d. Dec. 16, 1873 AE 35 yrs
Source: Waterbury Cemetery Transcriptions Washington County Vermont, 2000, Robert Morse, P. 163-165

Buried in Hope Cemetery, Waterbury, Vermont:
White, Lewis J.; 1841--1906
Hill, Lydia A.; his wife, 1835--1887
Source: Waterbury Cemetery Transcriptions Washington County Vermont, 2000, Robert Morse, P. 52

To summarize the children:

Isaac N. -- b. 1832; d. 1854; buried in Waterbury Center
Sarah P. -- b. 1833; d. 1897; buried in Waterbury Center; wife of R. W. Demeritt
Lydia A. -- b. 1835; d. 1887; buried in Hope Cemetery; wife of Lewis J. White
Elizabeth C. -- b. 1838; d. 1873; buried in in Waterbury Center; wife of David D. Sleeper
Julius T. -- b. 1841; enlisted 6 Nov 1860 at Boston, deserted 24 Sep 1861, whereabouts unknown
Delia M. -- b. 1844; d. 1861; buried in Waterbury Center

1. Isaac N. Hill b: Abt 1831 in Waterbury?, Vermont
2. Sarah P. Hill b: Abt 1833 in Waterbury?, Vermont
3. Lydia A. Hill b: Abt 1836 in Waterbury?, Vermont
4. Elizabeth C. Hill b: 12 Mar 1838 in Waterbury, Vermont
5. Julius T. Hill b: Abt 1841 in Waterbury?, Vermont
6. Delia M. Hill b: Abt 1844 in Waterbury?, Vermont