What are the advantages and disadvantages of DMs showing a map of the city to the players?

Both approaches are valid, and solve different problems for different groups.

Showing the map

• Showing the map gives players a menu to choose from. If they're having trouble spontaneously deciding where to go next, this is a really useful tool.
• A map can really give a wonderful visual sense of the place you're in. It can pin down the idea in the players' minds that they're in a particular city, rather than leave it abstract.
• The map isn't necessarily a literal map available to the player characters (something which may be unrealistic). It can serve as a non-literal representation of a place which the players could reasonably explore and familiarize themselves with over the course of a few days.
• The map can be used as a tactical representation of position or movement, such as a chase scene or ambush encounter. It can help answer questions like how far apart two different characters are when a fight breaks out, and how long it will take them to rush to one another's aid.
• There's a real cool factor in seeing a map of a famous locale, like the Baldur's Gate.
• It's an opportunity to make a hand-out.

Not showing the map

• The players may be overwhelmed with all the options. Instead of helping them decide where to go, it may hinder them.
• Some players will find it unrealistic to be shown a map. Accurate, detailed, up-to-date maps of cities just aren't readily available to most visitors to a fantasy city, and players may feel that being shown a map implies the unlikely existence of such a map in-world, which hinders immersion.
• The map may constrain player or DM ideas. For example, for plot convenience the DM may want to assert that the only potion shop in the town was destroyed in that last fight, but the map could betray the DM by showing the location of several other potion shops.
• A map available to all players makes it harder to have them get lost in the city, which hinders the DM if they wish to use this as a plot contrivance.
• The players might waste time exploring a city instead of following the plot or exploring dungeons.
• The DM needs to spend time learning the map to be prepared for the players' questions.
• The players may feel that they know the map better than the DM, such as by owning the book or a previous appearance of that location in another book or game. This may undermine the DM's air of authority when the contradict what the player thinks they know based on their copy of the map. (You can, of course, just insist that their map is outdated.)