There were a large number of mills in Ulster, so it’s not easy to trace the ones you are interested in. Do you know which townland(s) your ancestors had their mills? I may then be able to trace a little history about them. I have looked in Griffiths Valuation for 1864 at 3 townlands along the Callan river – Aghinlig, Keenaghan and Borough of Charlemont but don’t see any mills there at all.
The town where the linen museum is located is Lisburn, nor Lisbon. See:
If going to PRONI take your passport as photographic id is required to get your readers ticket. (Just takes 2 minutes).
You ask for other ideas. Can you be more specific about what you are looking for? Do you want some general suggestions for tourist sights in and around Armagh or something else?