What should a city have? Well, I have this here list of businesses kicking around that I have had for around 20 years (I know it's that old, cause it was printed on DOT MATRIX!). So, here we go:
Accountant, alchemist, animal dealer, animal trainer, apothecary (Druggist), bait shop, bakery, barber, bank, barrel wright, bath house, beautician, bindery (book maker), black smith, book shop, bordello, bowyer (bowmaker), brass worker, brewery, broom/brush maker, builder, butcher, cabinet maker, candy shop, carpenter, carpenter, carpet maker, cartographer, chandler (candle maker), cheese shop, cobbler (shoe maker), cooper (wooden cask maker), customs house, dagger shop, dairy, distillery, engineer, fabric shop, farmer's market, financier/lender, fishmonger, fletcher (arrow maker), florist, forger (gerneral metal worker), foundry(metal casting), freight company, furniture maker, fortune teller, furrier, gambling house, gem smith, glass blower, gold smith, granary, healer, herbalist, inn, jeweler, Kiln (shop for drying material), Lamp/Oil Shop, lapidary (gem polisher & engraver), lawyer, leather worker, limner (illustrator/painter), locksmith, lumber shop, magic shop, mason (stone worker), metal smith, mill, money changer, painter (of structure, not pictures), perfumery (perfume maker), potter, rope maker, sage, sail maker, seamstress, scribe, ship wright, silver smith, slaughter house, soap maker, stable, sword shop, tack shop, tailor, tannery, tavern, taxidermist, thatcher (thatch roof maker/repairer), tinker (household utensil fixer/seller), tool maker, toy shop, trading post, undertaker, wainwright (wagon maker), weaver, weapon smith, wheel wright (wheel maker), wood carve
Now, the above list is not exhaustive by any means. Other things cities need but not neccessarily be present is:
Sewer workers, town criers (herald news, etc), lamp lighters, porters/taxis (The existed in some form or another for centuries), street sweepers and privy cleaners (these people removed the waste from streets and outhouses), messengers.
In other cities, there would be slave dealers and other sorts dealing with aspects of our society that we no longer have.
Additionally, cities would have colleges, universities,churches, temples, public offices for senates, bureaucrat, mayors, nobility etc.