Dwarves, halfings, and gnomes are the most common of races to be seen throughout the world. From their perspectives the elves and half-elves can oft seem like giants. This can be cumbersome when elves visit the shorter peoples city states. When the short (well average) races visit the tall-folk the elven cities seem all the grander due to scale.
Humans
The time of Man has come and gone. Their great empires rose and fell in the blink of an eye as far as the longer lived races were concerned.
The tatters of the human race live outside the civilized areas of the City-states as hunter-gatherers, raiders, and in some cases, horse-lords. (Think Genghis Khan and the Mongols) The civilized races mostly stay within their City-states and thus have not felt the need to wage war on these lowly humans.
Humanity left many remnants from their height. Ruins scattered about the lands, old farms, villages, and cities. They worked the earth and wrung many parts of it dry. The world still bears the scars of Man, especially those of the War of Mankind. The humans meddled with many technologies and countless results of this meddling are still out in the world beyond the walls...
Elves
The elves focus on magic instead of technology. They experiment carefully and view their work as for the betterment of the world, despite what others may think. Ages ago, the elves created the half-elves and some say before that, the humans.
The dwarves saw this as the elves playing god and prompted a simmering anger against the elves that lives on to this day. Elven society does not look upon the half-elves with disdain, but still looks down on them as lesser creatures.
The City-state of Shi'darra houses another of the Elven creations, the Undying Court. These ancients elves have been transformed to live forever, serving as advisors for the Shi'darrans. The Undying are similar to the undead, but unlike zombies and ghouls are created with positive energy. Their exact nature is mostly unknown outside the elven race. Others focus on using magic to create wondrous items.
Half-elves
Half-elves were created for mysterious reasons in ages past. Their social dynamics and relationships with other races are complex but broad strokes are used to describe them here for simplicity's sake.
Half-elves often half strange appearances depending on their lineage. The elven half is the only constant, though human blood is often the other. Half-elves have split opinions on the other races. Some admire the elves for creating them, while others feel they must atone for their existence. Others still believe they were originally created for a purpose, be it to serve the elves, or to accomplish some other task depends on which group you ask.
Gnomes
The gnomish people are split. One sub-race is fairly xenophobic and keeps their distance from the others. The other sub-race thrived upon meeting the other races and are seen throughout the world with a fascination in learning all they can now that the human empires no longer oppress them. Some of the wizard travelers are gnomes so they can explore and learn.
Halflings
The halflings are friendly with everyone and often act as diplomats when racial tensions interfere. Used to life in the foothills in small villages until the War of Man drove them to the cities halflings can sometimes seem uncomfortable in cities.
Dwarves
Dwarves love gems. This lead their race to be amongst the most wide-spread merchants and leaders of commerce. Their presence is seen in almost all city-states and their straight-forward runes have become the standard trade language amongst the civilized races.
Dragonborn
After the defeat of Icingdeath, Tiamat took notice. Infuriated her spawn was defeated so easily by weak mortals.
To strengthen her kind, true, legendary dragons were bestowed the ability to spawn dragonkin. Now, where adult chromatic dragons are found, so too are dragonborn and kobolds. The Elites and cannon-fodder of the draconic hordes respectively.
Other Races
Hobgoblins, Orcs, Goliaths, etc. most races can be found somewhere in the world unless otherwise specified.