I see that we also share the spelling of our first names.I sympathize with your problems at the local restauarant (being called Corner, and all) but last summer when I was in Lurgan and told some locals (at the public library, a real estate office, and a funeral home) that I was a Corner and that my ancestors came from this town, I was told repeatedly that they had never heard the name - Cordner yes, but not Corner!
Familysearch, on the other hand, identifies a Samuel Cordner as a near relative of some Corners from Lurgan (back in the eighteenth century).It's impossible to know, however, whether this is a simple error since both names appear in Lurgan before this date, or the result of intermarriage between the Corners and the Cordners.Possibly, they were once the same family (with one name being original) and they split off like neanderthals and homo sapiens!We'll be the neanderthals, if that helps!
You might have an easier time gathering information in Lurgan since you may find Cordners who can tell you things.The town is rather small and largely without attractions.There is a single hotel on the main street, and several churches - Church of Ireland (Anglican), Methodist, Quaker, Baptist, etc - and three cemeteries.A small cemetery is behind the Quaker House, an older, now vandalized cemetery, called Shankill, is near the Church of Ireland and a newer, much larger cemetery, is about a mile down the road toward Craigavon and Portadown.There is a castle once owned by the Brownlow family that is, I am told, now the Orange Lodge.
It would be very worthwhile to spend some time in Belfast at the Linen Hall Library and at the Public Records Office of Northern Ireland (PRONI).Most of the surviving records are kept here in books and on microfiche.You'll need a fair amount of time though; the Irish are as bureaucratic as they are friendly.
What was the other place you were thinking of going?Lisburn?