Valyrians needed to adapt their constructions of cities to these disheveled terrains, as well as successfully connect them together through the many mountains and hills. It’s also important to mention that due to the high volcanic activity, lava would flow to lower ground in what could be called ‘rivers of lava’, but the valyrians built canals in order to control the path and flow through the cities ( those that did reach the cities, at least ). To cross these canals, long and tall bridges were made out of stone, capable of withstanding the constant scolding heat without eventually collapsing or loosing their form ( a feat achieved through spells, the same that allowed for the city to thrive so near to volcanic heat and lava–more on that on another hc post ). These same type of bridges were used to connect the cities in the peninsula though in a wider and far longer range, which would eventually be known as the Dragon Roads, spanning outside of the valyrian peninsula throughout the rest of the colonies and cities in Essos.

|| Note that the image on the left is from TWOIAF, which is from where I base this ||

As for the capital of the Freehold itself, tall ( or as referred to mostly, topless ) towers filled the city; many were built sitting on ground elevations, while others on valleys and lower, flatter areas. It’s there in the main towers and palaces where the noble families gathered. The tallest towers that rose from their respective palaces were the homes ( or one of the homes, in the case of Vaedar’s and some others’ family ) of dragonlords and their families. The highest level of these would be a cavernous space with wide openings, from which strong stone arms with various shapes extended, as well as platforms, so that dragons could perch themselves on them. The principal larger and wider bridges that served as the streets however ( the ones closest to the ground ), were almost always on the same height regardless, with the smaller and shorter ones above to connect different levels of the towers and other places.

The exterior appearance of these towers, palaces and bridges were often decorated with ornate patterns, sphinxes, and statues of all sorts of creatures, mainly dragons or similar. The stone used was of a darker color but it could vary between black, grey, pale and dark reds, and sand colors. They were often coated in obsidian and/or other ores mined from the Fourteen Flames, including gold and silver. The details of these decorations, such as the eyes of dragons for example, would be jewels like garnet and rubies and other gemstones. The unparalleled detail and skill with which these edifications and architectural works were made are possible thanks to dragonfire, and the use of magical spells that allowed the valyrians to manipulate the materials in whichever way or shape they wanted ( in a seamless manner as the stone was not cut or chiseled ).

However, as beautiful as the architecture was, it was also practical. The focus was to bring more comfort and commodities for the valyrians ( mainly their residences ), such as precious water from the nearby rivers in the peninsula. Aqueducts were built for this purpose ( see Roman Aqueducts ), transporting the resource to public buildings ( such as baths ) and also to private residences and palaces, which could also be heated through geothermal conductivity of the volcanic ability in the peninsula. It was also meant to be durable and resistant to the exterior heat exposure so that the interiors were not as hot as the outside. 

The decorations inside the palaces and towers were sometimes just as useful, for example, the candles of obsidian glass; which had the ability to be used as a means of swift communication to far off places. Statues and columns were very common in the interiors as well, along with the ornate patterns and forms made of different precious materials like silver and gold, as well as valyrian steel. Mosaics could also be appreciated, made from the same materials along with marble and dragonstone. The size of the palaces and towers were colossal in height and width, for it was meant to accommodate a large number of people when court was held, and if necessary, it was large enough for mature dragons to fit inside ( think the size of Drogon in the show ).

Undoubtedly, the capital city of Valyria was the most grand of all the valyrian cities but the same general modality and style of architecture was carried out to others in the peninsula, including the southern city of Draconys, where Vaedar was born. There, the palace sat on a hill overlooking The Summer Sea, with several towers rising higher, harboring some of the chambers with wide open balconies and extensions for their dragons. Though the purpose of the height behind these towers was so that only dragonriders would access them upon their mounts, there are bridges and long stairs that do allow others to reach the higher floors from the lower levels of the palaces. The Valarys residence in particular ( as a dragonlord family ), had its own interior gardens and pools, and rather wide and spacious courtyards where around three or four young dragons could land and expand their wings freely. Though other residences for noble freeholders were bigger than the more humble houses of lowly free citizens, the trend was for those belonging to dragonlord families to be more ample, higher, isolated and overall greater. It could be taken as a statement of the higher positions they have in the Freehold.

This is my headcanon on a concept of how Vaedar’s family palace ( House Valarys ) looked like ( art is my own ):

INFRASTRUCTURE

A majority of the structures, especially the more important ones ( the Anogrion, for example, and the majority of the palaces belonging to Dragonlord families ) were built from fused stone, or dragonstone as it was also called. It could last some say forever, and it was only with the destruction of the land below itself that these buildings were also destroyed. Due to the nature of the terrain, most of the city was divided in blocks or districts, some separated by canals of lava in the depths between the cliffs that could only be crossed via valyrian roads and bridges that connected them all. There were residential districts for the freeborn ( mostly apartment complexes ), commercial district ( the main bank was here, merchant's quarter, markets and shops ), temple districts ( buildings of worship of different religions ), entertainment districts ( art galleries, pleasure houses, outdoor dining, 'colosseum' like arenas ), public district ( the agora or central hub of trade and socializing, public baths, government 'offices' for public services, etc. ). 

It's in the public district where the Freehold's main palace or court is, where assemblies are held and the nobles gather for matters of governance. Closer to the face of the of the center and largest volcano more to the north, stands the Anogrion, the great temple of the valyrian bloodmages. It's there that blood and fire mages gather to tame and harness the power of the Fourteen Flames. As for the residences of the Lords Freeholder, they were built surrounding the city center, usually each as large as an entire block or district in territory, settled at the faces of cliffs. 

As pointed before, these structures were also meant to be practical. Along with Aqueducts, the palaces and homes of the nobles and those wealthy enough, also had plumbing. This allowed for faucets in their built-in tubs and their privy chambers to wash down their 'deeds, including access for hot water ( this was abundant, considering the volcanic activity ). Public baths were also worked with plumbing. 

|| Still a work in progress ||