Characters should strongly consider a "good" alignment.. There are lots of possible backgrounds for non-dwarven PCs.
Outsiders are not uncommon in Cragmire. The dwarven community opens itself to the outside once per year to facilitate a festive and bustling Gem market during which the city brims with a variety of visitors. Some befriend craftsmen over several years - and many of these eventually settle and are welcomed within the community. The market is critical to Cragmire's reputation and economy.
Cragmire also offers refuge to those persecuted by evil. It is an overwhelmingly lawful good place and extends the protection of its caverns to the deserving.
Powerful arcane magic users are very rare, however, within its confines. Those that are present are extremely discrete, especially following the recent (in Dwarven terms) betrayal of the old King (who was widely loved) by his arcane advisor. The current King keeps no magical counsel. The craft guilds do profit handsomly from enchanted weapons, armors and items made in Cragmire - and have started to pressure for a broader acceptance of those appropriately talented. They worry that a scarcity of magical means will eventually endanger their profits.
Cragmire has a small Royal Guard, any number of craft guilds, active Clerical groups. All of these entertain appropriate visitors - some more secretively than others.
Cragmire is the size of a major city. There are grand and ancient stone buildings. A river. Light is tunneled through crystal lined portals - the city is well and naturally lit in many portions. There are also museums full of the work of old artisans... The place is very established and is physically hospitable to non dwarven races.
Cragmire is relatively isolated, geographically, from its neighbors. But politically and socially intertwined. It is, in a way, an industrial power, providing its friends with arms and goods - in return trading for grains and other required natural products difficult to produce underground.
Some of those neighbors keep amabassadors in Cragmire, the ancient city is just too important to ignore and too difficult to otherwise keep an eye on. There are Humans, other dwarves. Even an (extremely) unlucky elf or two has found himself cast in this role - though none has been known to stay long.