In another thread I mentioned that the existence of adventurers would probably change how towns and villages interact with them. I mean... would you want people that could literally kill everyone you know without a lot of effort roaming around your town square? Probably not. Maybe over time the culture would change in obvious and non-obvious ways.
Yes, though I should first say that 'adventurer' is not a recognized profession in my world. The closest equivalent to adventurer as you use the word is 'mercenary' or 'sellsword'. Adventurer as D&D players use the word carries the connotation of hero or problem solver, and is positive in the way that the English word 'Knight' is (and not in the negative way that Ritter is in German). The word adventurer isn't in common parlance in my world. You'd never say, "We should hire adventurers." To the extent that the word is used, it means the same as the modern 'tourist'. An adventurer is a wealthy dilettante that explores the world at his leisure, and this sort of figure is as suspect as he is romantic - the idle rich, a sort of rich vagrant. 'Vacation' is not a word that would be readily understood either, nor would 'holiday' outside of its connotation of a 'holy day'. Life is too brutal for long vacancies from ones employment without cause.
So mostly the PC's in my game are either considered to be mercenaries or else actually are mercenaries. This both simplifies and complicates travel.
Most PC's begin the game without noble rank. As such they may or may not be entitled to carry weapons depending on the starting nation. Or their rights to carry weapons may be limited. In Hulshen only nobles can carry swords. In Talernga the only weapon a citizen is permitted to carry in the street without a license is a sword. Most PC's begin as citizens of a city, and so have papers indicating their residency and the rights that go with it. However, even if they have the right to possess weapons for their defense in the city, that generally doesn't extend to traipsing over the countryside armed. Armed individuals on the road will often be assumed to be bandits, and diplomacy checks/reaction rolls are in order if a patrol of the guard or a knight of the road finds an armed company moving on the road without permit.
There are several common exemptions. Nobles, clergy, and laity in the direct service of a temple generally have rights to go armed, and staves and knives are generally over looked as weapons unless the guard is feeling particularly abusive. So a good early excuse is that the group are all retainers of whatever cleric or knight happens to be in the party (if any). Once the group has a bit of money they can generally organize themselves as an official mercenary company under the protection of the local lord, and travel about and hire themselves out without getting in trouble (provided they pay their taxes). Also in more rural and wilderness areas, these laws tend to be rather laxly kept as people need to defend themselves from bandits in cases where the law doesn't have sufficient presence to do so.
Regardless of their ability to travel, getting into another city is an entirely different matter. They will be challenged and need to present papers identifying themselves, and explain their business in the city. They will likely have their goods subject to inspection, and certainly will if they have baggage, carts, mules, or a train of horses. As mercenaries, they may be forbidden to enter the city at all unless a good reputation proceeds them or they are here on business from some authority figure the locals respect. Or they may be restricted to only a certain number entering the city and then unarmed. Of course, if the city happens to be in great need, mercenaries on the other hand might be just the thing.
Wizards are special circumstance everywhere. By common law, wizards of any rank are entitled to honorifics - Your Potency. In practice, if you insist on your honorific though, you better be a darn good wizard - by which I mean some unthinkably high level like 5th or 6th.
They also have rights to privacy and dignity normal travelers don't - you don't paw through a wizard's baggage! On the other hand, they absolutely MUST declare themselves to the guard and register when arriving in the city. Failure to do so is generally punishable by death. A wizard cannot legally conceal his ability. In many places they must adopt dress that unmistakably identifies them as a wizard at a distance. A city will not bar entry to an unknown wizard. Ever. It's too risky. They may plot his death when he falls asleep, attempt to drug him, or otherwise plan subtle murder but they aren't going to risk a wizard's curse by denying him hospitality.
Clerics are likewise a special circumstance. Generally speaking, for similar reasons, no city ever bars entry of a cleric - it's not worth risking angering some god. However, in general, the rights of a cleric who is not a servant of one of the 6-20 official divine patrons of the city which the city officially supports and engages in communal worship and offerings to are rather limited. In most cases, you aren't allowed to spread 'an alien doctrine' to a city. Trying to win converts will get you politely shown the door by some Templars at best, and executed by the cities' existing clergy at worst. If you want to openly preach your faith, you need the approval of the city. In most cases, by custom however a cleric is allowed to beg for his substance and bless those that give. In a few cases though, hostility between two sects is so great that there exists basically an ecclesiastical war between the followers of two deities. If you go into a town where your rivals sect is openly supported, they'll nod at you politely but you are basically declaring war on the local temple and they will respond in kind. Your death (our theirs) will be considered to be a matter between the gods and not really a matter falling under the cities jurisdiction.
Presently, the PC party has one player that obtained noble rank in play. He previously had some freedom to go about armed as a Templar of the Order Hospitallers of Aravar, but now as Sir Gorinthar, Templar of the Order Hospitallers of Aravar, Knight of Amalteen, famed dragon slayer and rumored saint he has considerable freedom. He could pretty much say something like, "I'm on a sacred quest. Stand aside and leave me to my business.", and most people would do so - though they'd send word up the chain of command concerning the unusual behavior. Likewise, the party cleric has obtained the robes of a full priestess of Showna, and is properly addressed Reverend Mother. Since she has the favor of the High Priestess, if she really wanted to challenge authority she probably could do so - no one really wants to see Showna upset. The other party members are basically free agents, but society treats them as variously the retainers of Sir Gorinthar (or perhaps his Gentlemen-in-waiting or Gentlemen in Arms), or retainers of His Potency Master Aden of Amalteen, or of His Excellency Falster Dikelgard, the Most Benevolent Despot, Sovereign Prince of Amalteen on the assumption that they must be somebodies servants. As such, they inherit some measure of the authority and respect of whatever person its presumed is actually commanding them - even though the reality is they've basically been told 'you are on your own'. And finally, since the party is known to have been shown the favor of Their Majesties, the Hurin and Hinga of Talernga, there is a general assumption by everyone of low rank that these are Important People and its best to show some diffidence and give them the benefit of the doubt.
It's not always been like that.
And if they were to leave and come back with about twice as many levels, it wouldn't be long before everybody was deferring to them out or respect or fear or both.
