The first trace of William Allis after landing was in Mount Wollaston (afterward Braintree) in 1632. That town, comprising 50 square miles, was surveyed and laid out by him before 1634, and during that year, by order of the General Court, it was annexed to Boston. Large tracts of land were granted to certain inhabitants to settle in Mount Wollaston and William Allis received 12 acres on February 24, 1640. On May 13, 1640, the inhabitants of Mount Wolaston were incorporated as the town of Braintree and, with Dorchester, Dunham, Hingham, Natasket and Roxbury, were incorporated to form the city of Boston. This was also the day William is listed as a freeman.
Drake’s History of Boston, 250.
Pattee’s Braintree & Quincy, 11.
Massachusetts Rec., vol. 1, 291.
Winsor’s Mem. History, 116, 217, 234
He is variously given as being on the Mayflower in the Winthrop Fleet (but the Winthrop Society does not accept this) and on the Lyon in 1632 (that was Richard Allis).
He performed weddings in Braintree in 1656-57, including that of Nathaniel Mott and Hannah Shooter. (NEHGR 37:286)
Went to Wethersfield where he was one of those who left in 1660-61 to settle Hadley, north along the Connecticut River in Massachusetts. His home lot was on the west side of the main street in the center of the settlement. The present meeting house, town hall and Congregational parsonage are all on the lot which was assigned to William Allis. That part of Hadley eventually became Hatfield in 1670 then the far north was incorporated into Whately in 1771. home lot was on the west side of the main street in the center of the settlement. The present meeting house, town hall and Congregational parsonage are all on the lot which was assigned to William Allis.
He was a member of the committee which was appointed by the town on March 7, 1673, and authorized to regulate the settlement of Deerfield. In 1674 was one of those commissioned to lay out Swampfield (Sunderland). In 1676, he was a captain for Hadley at the Falls Fight where his son William was killed. A later attack known as the Hatfield Massacre took place Sept. 19, 1677. His wife Mary was one of those killed and his granddaughter Abigail was taken captive. (http://freepages.genealogy.rootsweb.com/~streeter/allis.htm)
He held a number of offices including deacon, cavalry lieutenant, justice of the peace and selectman. At his death his estate was inventoried at £496. It included linens, brass and pewter items, furniture, livestock and four plots of land.[ 
From Massachusetts Genealogy Records 1600s-1800s, Pioneers of Massachusetts, page 16:
ALLIS, ALLISE, ALLYCE, ELLIS,
William, Boston, Braintree, 1639; frm. May 18, 1640; deacon. Had a
lot for 3 heads, 24 (12) 1639-40. Wife Mary d. Aug. 10, 1677; he m. 2.
June 25, 1678, Mary, dau. of John Bronson and widow of John Graves of
Haddam, Conn.; ch. John b. 5 (1) 1641, Samuel b. 24 (12) 1646, Josiah d.
15 (8) 1651, William b. 20 (8) 1651, Mary b. 25 (8) 1653. William b.
Jan. 10, 1656, Hannah, (m. William Scott). Rem. to Hadley and then to
Hatfield; Lieut.; asst. of court, 1676.
Will prob. Sept 24, 1678; beq. to wife, and to ch. John, Samuel,
Hannah and Mary.
Savage’s: WILLIAM, Braintree, had gr. from Boston of twelve acres for three heads, was freem. 13 May 1640, by w. Mary had John, b. 5 Mar. 1642; Samuel, 24 Feb. 1647; Josiah, wh. d. 15 Oct. 1651; Josiah, again, 20 Oct. 1651; William, 10 Jan. 1653, wh. d. at 9 mos.; William, again, 10 Jan. 1656; beside two ds. Hannah, wh. m. 1670, William Scott; and Mary, wh. d. unm. 1690; rem. to Hadley 1661, on the W. side of the riv. now Hatfield; was selectman 1662, lieut. of the cavalry, a deac. and his w. d. 1677. He m. 25 June 1678, wid. Mary Graves, made his will 2 Sept. at Hartford, 4 days bef. his d. 1678. His wid. Mary, d. of John Brownson, whose sec. h. John Graves, was k. so shortly bef. as 19 Sept. 1677, had in 1668 been wid. of John Wyatt, and was happy to gain for fourth h. Samuel Gaylord, m. 1682. His s. William was k. in the Falls fight, 19 May 1676. Sometimes his name appears Allice.