Sorry about coming into a bit late. Actually this is a good question and thanks to Bushido for bring it up.
A good way of looking at this is from the opposite side. Who would be allowed to carry weapons and where would they be able to carry them?
City Guard or the Night Watch. These would be employed by the nobles/city council to maintain the peace and pursue those observed in criminal acts. Because of the nature of their job they would need to carry obvious weapons. Also, the job would allow them to travel throughout most of the city.
Nobles and their retainers. The ones with the power to make the laws get to create the loopholes in the law. Because of their position and status these individuals would want to ensure that they are able to protect themselves, or have people around to protect them. Again these would be obvious weapons used as much as a warning to tell others to stay away. Being noble the individual would be able to go where they want to go.
Priest/Temple Guards. Historicaly temples aquire wealth and goods and at some point those need to be protected. Usually they would patrol the area around the temple and be restricted to those areas. They would also serve as the body guards to those preists who need to travel through the city on business. How well they are armed and armoured would depend on the wealth of the individual temple.
Merchants. If your carrying, or have acess to, large amounts of money you want to be protected. The question here is do the merchants supply the weapons and armour? If the employer is cheap then the guard might need to supply his own equipment. If he is wealthy and wanting to establish a presence then his guards might be supplied with matching uniforms, weapons and armour. these guards might also be expected to do security around warehouses, stalls in the market place, and caravan duty. all of which might give them free run of the city or cities.
All of the above would be jobs that would allow adventures to carry their weapons in public. They might need to dress in a specific color, have papers, or a symbol to show who has employed them and that it gives them the right to carry particular weapons. The downside for the characters is that this form of employment might require them to be on call and agree to a set amount of time for the employment.
Other groups that might fall into one of the above groups could include; officers of noble birth, soldiers stationed in a city near the battlezone and, mercenaries hired by any of the above groups.
A good collection of books to use when trying to get an idea of what life could be like in the Hyborian setting can be found at;
http://www.amazon.com/exec/obidos/tg/detail/-/0060908807/qid=1129819053/sr=2-1/ref=pd_bbs_b_2_1/002-4008761-8095258?v=glance&s=books
http://www.amazon.com/exec/obidos/tg/detail/-/0060920467/ref=pd_bxgy_text_1/002-4008761-8095258?v=glance&s=books&st=*
http://www.amazon.com/exec/obidos/tg/detail/-/0399502580/ref=pd_sim_b_5/002-4008761-8095258?%5Fencoding=UTF8&v=glance
I've used all three of these in helping establish background for my fantasy rpg settings.