Geilston Bay (pronounced both "Jeels-ton and "Geels-ton", other pronunciations also possible) is a largely residential suburb of Hobart between Risdon Vale, Shag Bay, and Lindisfarne, in the City of Clarence located on the Eastern Shore of the Derwent River, taking its name from an inlet of that river of the same name. The inlet and locality were sometimes known by the alternative name "Limekiln Bay" on account of lime kilns which operated there between approximately the 1830s and the 1920s, the remains of which remained visible for some decades thereafter; another early name for the Bay was "James's Bay". The present suburb name derives from an early land holding "Geils Town" in the region purchased by Andrew Geils, Commandant of Van Diemen's Land (Tasmania) for a brief period in 1812-1813, who subsequently left his Australian holdings behind when he moved back to Scotland.

The nationally significant Late Oligocene (or early Miocene) "Geilston Bay Local Fauna" fossil find originates from this locality. Fossil mammal remains at this site were discovered by limestone quarrying activities in the 1860s and sent to the British Museum in London for further analysis, where they still reside. However there are no surface indications of the location of the site today, which lies buried by landfill under the playing fields of the former Geilston Bay High School.

Prior to the British colonisation of Tasmania, this land, part of the Oyster Bay region, had been occupied for possibly as long as 35,000 years by the semi-nomadic Mumirimina people. Mouheneener shell middens can be found in the area between Geilston Bay and Shag Bay, along with the remains of an Aboriginal rock shelter.

The area now known as Geilston Bay was initially settled via a series of land grants of around 50-70 acres each to pioneer settlers including William Parish, Michael Mansfield, William Collins, and David Wakefield over the period 1806-1808. Parish, a former highwayman (armed robber) in England, had previously been transported to Australia, served his sentence, returned to England, and eventually came out to Australia once more in the role of a convict overseer at New Town from 1805, before being granted "70 acres on the eastern shore of the Derwent" in 1806. Mansfield, apparently a free settler, was granted "50 acres lying and situate on the River Derwent, Van Diemen's Land, on the East side of the Derwent" in 1808. In an 1809 "Muster of Settlers", Parish and Wakefield are not listed (perhaps their holdings were too new to have been developed) but Mansfield's holdings (with a wife) are described as "50 acres, 13 in wheat. 3 cattle, 12 sheep, 10 goats, 1 swine", while Collins' holdings are given as "50 acres, 6 in wheat. 2 cattle", both in the region known as "Risdon/Clarence Plains". Conditions for both farming and general dwelling would have been fairly primitive at that time, with few roads, travel to Hobart being only by boat, and constant threat of robbery by bushrangers: Withington (2009) notes that in February 1808, Parish was robbed by the violent bushrangers Richard Lemon and John Brown, the pair being apprehended by Mansfield with assistance of two others the following month, with Lemon resisting and being shot dead, and Brown captured and eventually hanged for his crimes in Sydney.

Whatever modest farming ventures these new settlers had managed to set up were disrupted by the arrival in Hobart in February 1812 of Colonel Andrew Geils, newly appointed Commandant (acting Governor) of the settlement of Hobart Town, at that time established barely eight years earlier. Geils, a military officer with aspirations to an eventual government role, was the son of a General Thomas Geils who had purchased a number of country estates in the latter's native Scotland, and it seems that the son planned to follow in his father's footsteps in his new adopted colony, purchasing and then developing the "Restdown" homestead at the original Bowen settlement site at Risdon Cove; via a land grant to his wife, he also owned property in Pittwater. At the present location he acquired and consolidated some 200 acres the same year by purchasing the grants of Mansfield, Parish, Wakefield and Collins, who then relocated elsewhere; possibly he also purchased other land in the district, since by 1867, when the property had long since passed out of Geils' ownership, a second parcel of land listed as "1515 acres, known as Geilstown" was also being offered for sale (see below). Under circumstances that have not yet been clarified, the holding and/or surrounding area then became known as "Geils Town".

Unfortunately for Geils, his appointment as Commandant was for one year only and his subsequent aspirations to be appointed Lieutenant-Governor of the Colony following Thomas Davey were thwarted by Governor Lachlan Macquarie, in whose opinion Geils' behaviour while in Office rendered him unsuitable. Geils decided to resume his military career and accompany his regiment to Ceylon in 1814–1815, apparently never seeing Tasmania (then known as Van Diemen's Land) again: in 1815 his father died in Scotland leaving him one of the latter's estates, that of Dumbuck in the parish of Old Kilpatrick, to which Geils appears to have located by around the end of the decade, having a daughter there in 1821 and a new house constructed for himself and his surviving family, Dumbuck House (still in existence and now a hotel), residing there until his death in 1843.

During his short period of active involvement with his Tasmanian properties, Geils (or possibly his agents) appear to have established a farm on this particular holding known as "Geils Town Farm", described in 1818 as "200 acres opposite New Town", and later (April 1824) as "Geils' Town Farm ... to be let, for a term of years, a farm of 500 acres, called Geils' Town, about three miles from Hobart Town, on the Derwent." Ward's account, however, suggests that Geils spent most of his efforts (financial and time wise) developing his property "Restdown" at Risdon Cove. Eventually in 1818 and 1821, presumably in association with Geils' move to Scotland, his Tasmanian properties were offered for sale but apparently not selling at that time; eventually an offer for their purchase was made in 1832 by Thomas Gregson, an 1821 arrival in Hobart Town, briefly Tasmania's second Premier in 1857, and eventually a major landowner on the eastern shore of the Derwent (Gregson was also responsible for naming of the adjacent suburb "Lindisfarne"), with Geils Town Farm continuing to be leased out to other parties for his period of ownership and beyond.

Gregson's purchase of the Geils properties at "Geils Town" and Risdon went through and by 1838, Gregson's tenant in the present area appears to have been one John Price, who had arrived in Hobart in 1836. Price, who also had interests in a timber felling operation on the Huon River and was shortly to marry the Lieutenant-Governor's niece Mary Franklin, purchased land at Lindisfarne and appears to have been renting the Geilston Bay property: a portion of a letter of that year written by Jane Franklin, wife of the Governor reads "[Price] in the meantime commences building another [house] on his rented property, for which he is to have a suitable reduction in rent from his landlord Mr Gregson. He is cultivating the land and burning lime for which he has an easy market in Hobart Town." Price, who had a number of high ranking civil positions in Hobart over the next few years, resided in Tasmania until 1846 when he was appointed to the position of Civil Commandant of the Norfolk Island penal settlement; following his departure (or even in the years preceding it when he may have been busy with other duties), details of the operator of the quarry and/or the associated farm are not presently known.