Chuig, go, go dtí
I saw that:
Chuig is used when going to an event or a person. Tá mé ag dul chuig an cheolchoirm.
go is used when going to place-names that are not preceded by the article. Chuaigh mé go Baile Átha Cliath.
go dtí is used before place-names and any other nouns that are preceded by the article. Chuaigh mé go dtí an siopa.
Is this correct, or is there important, additional information I should know about?
Chun (if not also chuig) can also be used like go dtí with placenames with articles, e.g. chun na Fraince.
It's also worth noting that they generally don't say chun in that sense in Connemara. And also that chuig, in Connemara, is pronounced ag, with the same inflections.
Go raibh maith agat. Do you know if that is dialect specific and, if so, what dialect uses it?
This stuff is very dialect dependent. In Munster "go (dtí)" is used, unless you're using a specific verb that always takes another preposition, so you'd say:
Chuas go dtí an dochtúir = I went to the doctor.
There is "Chun" but it really means toward or is used with specific verbs:
Bealach chun na scoile = the road toward(to) the school.
Note: Chun however most often means "For the purpose of" or "in order to" in Munster Irish.
go dtí - until. I went as far as/until a specific place but no further. "Chuaigh mé go dtí an siopa" would indicate you went as far as where the shop is physically located and stopped there, you didn't actually go inside the shop. Might only be an Ulster thing and not actually apply in other areas.