A relatively small subset of English speakers in Southern England in the 19th century and early 20th centuries, including the upper class, used I shall and you/he/she/they will as a default for future actions. The use of I will and you/he/she/they shall meant something beyond plain futurity, although the rules for exactly what it meant were fairly complicated.
See this for an explanation of that system of tenses.
As far as I know, nobody uses this system anymore (except maybe some historical novelists). I suspect it was too complicated to survive for a long time. Let me note that in that system, your example
I will never go there,
was a possible sentence; it was a much stronger statement than "I shall never go there."
It probably would have meant something like "I utterly refuse to go there."
In the U.S., we tend to use will for everything except first person questions and legal documents.
For first person questions, shall we is a suggestion, an offer, or asks for an opinion.1 and will we is a question about facts. So you would generally say
Shall we go to a movie?
Will we go to jail?
In the U.K., shall is used more often than in the U.S., but I don't know the current rules. BBC's Learning English seems to have a good explanation here. Summarizing, it says that for statements, people use both I/we will and I/we shall in the first person, and that there is usually no difference in meaning; for first person questions, the same rules apply as in American English.
1 Although lots of Americans don't even use shall we in these situations. They don't use will we, either. They might say something like Do you want to ..., Do you think we should ...