YouTube has plenty of videos for making such maps. Just pick a style to use from them.
When I do a city map - I only do Early Modern+ games - I start off with what kind of access does this city have for Land (highway), Sea (Port), Air (Airport), and Internal (Streets & Mass Transit)? Rank that access 1-10. Does it have several major interstates coming into the city? It should rank high for Land. Is the airport small and cramped? It should rank low for Air. Is the subway system TEH SUCK? Internal is very low - etc. Then place these into neighborhoods. The interstate comes in from the west and skirts the city center before leaving to the south. The Airport is on the bay, hemmed in by tall buildings on three sides. The seaport is here in this commercial district along the bay.
Then I go neighborhood by neighborhood. What is this neighborhood? Residential? Commercial? Governmental? etc. So I choose, say, residential. Then what kind of residential - Dense (high rise rentals), Urban (low-rise rentals), Suburban (single family homes), etc. How nice is it? New? Old but spiffy? Dilapidated? Slummy? How big is it? How important is it to the city government? How do the cops see this neighborhood?
Then I ask: What are other neighborhoods are accessible easily from here? This helps interrelate everything. I usually draw a relationship map from this, like a schematic. Some games that's good enough. I would look at similar neighborhoods in similar cities. Houston TX, New Orleans LA, Galveston TX. See what they look like - maybe use photos of these neighborhoods to illustrate to the players. I might draw in important streets - high volume traffic or social importance. Spot interesting things - parks, playgrounds, theaters, shopping areas, restaurants, etc. You can always add these in as you play. I wouldn't bother drawing and naming side streets. You can always just describe them, but keep a list of names and make notes when you use these names. Otherwise you could end with three Charles Streets - which *could* happen, but is confusing. It's better to note "Charles Street - in Livingston Park, residential side street, bodega 'AJ's', donuts! Nicer than most streets in LP. Vietnamese restaurant 'What Dat Pho?' on corner Highland." That's what you need for roleplaying.
Added: Whups! Sorry! Misunderstood the "not for roleplaying" bit! I thought it was not for a published roleplaying game - just internal use. Then let's say this is all for developing the city, and actually drawing the map is techniques the other posts can help you with!