"...[W]ould [it] be OK to just give city map to players for nothing?"
Yes. If you think that discovering the city slowly through exploration doesn't add to their and/or your fun, then handing them the map or menu is a perfectly valid way to handle towns. I often list places in a town when the party arrives menu style. I don't bother with town maps, unless it becomes important -- i.e. something splits the town in two. The outline/menu make adding places if the party asks for a place to buy something I wasn't expecting more believable, as I don't pretend my spoken "menu" is everything in town, just the highlights. I also keep some store information for common types of shops I can drop into any city, in case they want a forge or a magic shop. Once I place that shop in a city I move the description to the city, so I don't accidently have two identical shops with identical product offerings in two towns.
" Will there be any unintended side effects of this approach?"
There aren't any unintended side effects, all the side effects are the known -- the players know where things are, and don't have to discover them, but they also don't get the "fun" of discovering them either.
"What is the usual approach here?" and "What are the positive and negative effects of doing [each]?"
It is not a Binary Option. There are more than just map and no map options.
- Like I said above, I typically don't even have town maps. I have a short description and outline of the buildings and places. I read the party the names of the most prominent and relevant places, as potential places they might want to visit. The benifits is that it is more flexible, as you can add places in the town if the need arises. The downside is that you can lose the physicality of location of the buildings (unless you sorta plan it out and add notes about "down the river from..." or "to the east of ...").
- I've seen streamers use a table size city battle map (1 sq = 10ft. instead of 5ft.) and "fog of war" uncover the map (construction paper and/or PostIts) as the party moves through. It is slightly more work to create the larger maps, and the interruption of removing the "fog" can slow down play -- but the feel of discovery is more organic like it would occur in real life.
- There is also using a battle map, and unvelling the whole thing when they arrive. This requires a smaller town, and is more work, especailly if your battle maps aren't just paper, but 2.5D or 3D. This can allow for some truly beautiful table top sets, but you limited by the table size (thus have to have fewer places in town) and the preparation requires more time for setup.
- The core D&D modules typically have a map and text descriptions so you can do either or both. They typically also provide a player map and a DM map (with where encounters and such are) so that you have a map that is safe to hand the player. Handing over a map is nice in that creates that physicality of where things are, and you can better judge "travel time" in the city between locations. The downside is that there are a set number of buildings on the map. While you can turn an unlabeled building into something you need for story or player request, "Sure, that one right there is the bakery." It is more obvious it wasn't planed for (can hurt some player's suspension of beliefs -- I've heard), and if all the buildings on the map are taken up, you're left to hand-wave or build new map at the fringes.
- When my players got to a town I didn't expect them to reach or want to go to in a session and hadn't planned the details of that city yet, I've lead with a vague description of typical architecture and/or types of people they see on the street. Then I've asked them "What do you want to do?" They were like, "Oh, it's a town. Is there a place to buy..." and "Is there a tavern to ask ask around about..." and it worked out quite well. It meant more on the spot pressure for me to write notes, so I know who is the town if they come back.
Do What Works
So the thing that works best for your game, prep and players to make the game as smooth and fun as possible. If that means exploration and discovery, giving them a town map, or something in between, then do that.