Inspiration will strike characters at various times and will mean that they have an artifact that they want to make for someone who is willing to fund their work. One type of those is the Adventurer, and they search for artifacts.
The adventurer is a somewhat unique type of inspiration in that it is much less clear what this person will present to you in the end. Instead, this is a character who knows that they want to undertake a journey to explore and look for an interesting thing for you and your court.
How far away a region that an adventurer will want to target with their expedition is mainly dependent on their skill and generally the adventurer already knows where they want to head when they appear to seek your patronage. A highly skilled adventurer might leave the choice of destination up to you.
Regardless of what destination an adventurer will aspire to travel to they will ask you what type of thing they should be looking for. You can let them decide for themselves as their adventure unfolds or you can ask them for a general category of object from the get-go.
Depending on the adventurer skill you may even be able to ask them to look for something unique, which will make them actively search for one of the unique historical artifacts that exist in the game. Nothing is entirely certain though, and even an adventurer of low skill might run into something interesting if you tell them to keep an eye open for anything interesting, it is just less likely than asking someone with higher skill to do so.
When given free reins you may also end up with a piece of armor, or a weapon from that region, with a visual appearance and local technique to match. There is also a small chance that an adventurer who is told to trust their own instincts could return with something more rare and unique.