The earliest known reference to the battle between the Welsh and the Saxons on the River Conwy is from an entry in the Harleian Chronicle for the year 881:

'Gueit conguo? digal rotri adeo' (Gough-Cooper, a442.1).
Translation: 'The battle of Conwy; the avenging of Rhodri by God' (Dumville, 12).

Rhodri Mawr ap Merfyn Frych was the king of Gwynedd (Bartrum, 2009, 637) and the leader of the Welsh forces was most likely his son Anarawd, who succeeded him as king of Gwynedd (Bartrum, 2009, 16). The reference to the avenging of Rhodri, who had been killed by the Saxons in 878, suggests that the Welsh were victorious against the Saxon, almost certainly Mercian, enemy. The Brutiau add nothing further, but a thirteenth-century collection of Welsh Genealogies provides additional information:

'Tudwal the Lame son of Rhodri was wounded in the knee in the battle of Cymrid Conwy, when the sons of Rhodri fought Edryd Long-Hair, King of Lloegr, and from that wound he became lame. And for that reason his brothers gave him the chief churches of Gwynedd' (Bartrum, 1966, 101).

Edryd Long hair is a reference to Aethelred of Mercia (Charles-Edwards, 490?1). Robert Vaughan of Hengwrt (d.1667), who owned the genealogical manuscript noted above, expanded upon it further in 1663:

'Anarawd was not idle, but gathered together all the strength he could make; His Army encamped neare the Towne of Conwey, at a place called Cymryt, where He and his Men making gallant resistance against the assaults of the Saxon power, at length after a bloody fight obtained a compleat Victory. This Battel was called Gwaeth Cymryt Conwey because it was fought in the Township of Cymryt hard by Conwey, but Anarawd called it Dial Rodri, because he had there revenged the death of his father Rodri. In this battle Tudwal the sonne of Rodri Mawr received a hurt in the knee, which made him be called: Tudwal gloff or the Lame ever after; his Brethren to reward his valour and service gave him Uchellogoed Gwynedd' (Prise, 49-50).

Cymryd (SH 7920 7586) is situated on the west bank of the River Conwy, 1km south of Conwy, and a location in this vicinity would seem to fit the available evidence.

RCAHMW (Battlefields Inventory), Nov 2016

Bibliography
Bartrum, Peter C., A Welsh Classical Dictionary: People in History and Legend up to about A.D. 1000 (Aberystwyth, National Library of Wales, revised edition, 2009).
Bartrum, Peter C. (ed.), Early Welsh Genealogical Tracts (Cardiff, University of Wales Press, 1966).
Charles-Edwards, T. M., Wales and the Britons 350?1064 (Oxford University Press, 2013).
Dumville, David (ed. and trans.), Annales Cambriae, A.D. 682?954: Texts A?C in Parallel (Cambridge, Department of Anglo-Saxon, Norse and Celtic, 2002).
Gough-Cooper, Henry (ed.) The Harleian Chronicle: Annales Cambriae, The A Text from British Library, Harley MS 3859, ff. 190r?193r, online edition.
Prise, John, A Description of Wales (Oxford, 1663).