The sentence indicates that the action of visiting has not occurred over a period of time in the past. "For" is the correct preposition used to express the duration of time, such as "for a year," "for a long time," etc. In this case, "for a long time" correctly expresses the duration of time that has passed without the visit.
- "At" refers to a specific point in time or a location, so it would be incorrect here.
- "In" is used to indicate a period within which something happens (e.g., "in a week"), but it's not the right choice for expressing duration of time.
- "With" implies accompaniment, which doesn’t fit the context of the sentence.
- Use "for" to indicate a period of time (e.g., "for a long time," "for two hours").
- Avoid using "at" when referring to a period of time, as it typically refers to specific points in time (e.g., "at 10 AM").