I have gone to Seoul three times.
Is perfectly grammatical, although we would probably say, "I have been to Seoul three times," in most contexts. However:
I have gone to Seoul three times in search of the best bibimbap.
Sounds more natural to me than "been," because "to go" is more purposeful and less passive.
I have gone to Seoul three times and returned home.
Sounds odd to me, but it could work, depending on the context. There are two issues, I think:
The construction of the sentence implies that you went to Seoul three times, and then you returned home; perhaps the trips to Seoul originated from somewhere else, not your home city. If that's what you mean, we need more context to establish that.
In English, "I went" usually implies "and returned." This is not true in many languages (e.g., Japanese). This is not natural in English:
Q: Where did you go last week?
A: I went to Seoul and returned home.
It sounds odd, because you're stating something that is automatically implied. However, this would be natural, albeit slightly formal:
A: I went to Seoul and returned home late Friday night.
(In casual speech we'd say "got back late Friday night.")