I want my advanced culture to have stone houses but I cannot think of a reason why they would keep this old fashioned method. What can I do to convince the czar of this land to use stone for building instead of metal or lumber?
Stone Buildings are Hard to Burn
This is no joke- if you want your home to be resistant to fire, use stone or ceramics (clay) to form the load-bearing parts. As a small anecdote: I have lived in Europe, and once in a mostly stone home, which experienced an electrical fire. What did the fire department do? Tell us to simply keep flammables away from the fire, and let it burn itself out. Did it work? Yes, it did. Our house, nor the things in it, burt (aside from some electrical wire).
Also, stone countertops can easily take excess heat from hot pans and such. Most people consider this ability a definite perk.
Stone can be really handsome. Some people like the way it looks. Some people really like how some rock looks, and rocks come in a variety of shades, textures, and colors. They can be pounded or eroded to become smooth, or kept rough and craggily. As far as an artistic medium goes, it's pretty broad and versatile even in natural or lightly-manufactured forms.
Refuge From Things
Imagine the relief you feel from a cool tile floor on a summers day. Now, make your whole house like that! Stone can be a good insulator, but expensive to shape and put together. It's good for extreme hot/cold environments. Obviously, in a cold environment, you'll need to heat it (and maybe use many floor rugs), but in a hot environment, it's great! Additionally, due to the fact that it takes a lot of energy to heat/cool your stone, a home of stone will experience thermal lag, so your home is warmest at night, and coolest in the day.
We should also mention that the weight of stones helps a building withstand high winds. If you're afraid of your house being blown away, make like the third little pig and make your house out of bricks, or stone, or something equally heavy. Also, this same argument may apply to invaders, raiders, and traitors.
"Environmentally Sound" Building Material
Some areas of the world have lots of rocks. Putting them to good use has the added benefit of making your homes very recyclable. A rock taken from an old building can be just as useful as a rock taken from the ground. Rejected building rock can be ground up and used in cement, or gravel walkways. Rocks are everywhere, so procuring them is rather cheap. Demolished homes would have nothing nasty in them- like asbestos. (Unless you actually put asbestos rocks in there... then it has a lot of asbestos!)
I never got why in the US, where storms are so common, the houses are built with lumber. In middle europe nearly every house is build of stone or concrete. This has the advantages mentioned above (fire resistance, thermal lag, etc...) and in addition a good protection against storms and snow. Also I as far as I know, middle Europe is quite an advanced culture, so I see no reason why an advanced culture shouldn't build houses of stone. If anything I consider using wood as building material is "less advanced".
Durability. Modern light-frame residential construction is designed to be exactly as strong as it has to be in order to reduce costs, and if they went without any maintenance they wouldn't last 30 years. The bones of a light-frame home could last a century or more, but that depends on the exterior holding up to the elements, something most stone buildings can handle as a matter of course but most modern buildings require re-sealing every few years and re-roofing every 20 to 30.
If cost were less of an object (in a society with sufficient technology, the logistics of stonecutting would make assembling a building out of carved blocks less demanding than today), building a home durable enough to pass on to your children and their children would be worth something. It's counterintuitive that as our technology grows, we're moving past the need to be mobile; many jobs can literally be performed from anywhere, and of the ones that do require travel, most are local in scope (maintenance, local delivery etc). That makes a durable home a better investment.
In extreme environments, stone provides a thermal "battery" to moderate temperature swings. During the day in a desert, the stone will absorb the heat while the interior of the building stays cool. At night, the warmth gradually seeps into the house and keeps the interior warmer than the cool outside. (If you don't have stone, the same effect can be had with massive masonry walls, adobe or rammed earth as well). In cold climates, the heat from the hearth will be retained in the stone after the fire burns out, keeping the interior warmer without such a large expenditure of fuel.
Stone is also relatively inexpensive (it is the stonecutting and dressing that makes it expensive), long lasting and sturdy if built properly, all bonus points for people who build with stone.
Instill in your czar the idea that the old ways were better, that we are in danger of losing important history, and it is incumbent on us all to preserve the past by retaining its sound architectural techniques. Stone castles have stood for hundreds of years; those newfangled wood-frame houses don't last nearly as long. And steel? Hard to make, hard to work with, messy.
Combine liberally with a sense of fashion. Since he's the czar he probably has a great deal of sway with public opinion (controlling the press and all that). Use that. Make people want to preserve this aspect of their history.
But progress is good too.
We aren't just old-fashioned, you must assure your czar; we are also looking out for the future. Stone is available without the environmental impact of deforestation or steel mills. Stone is also durable and long-lasting, so you pretty much only need to quarry new stone for additional construction — houses you've already built will stay put, and if you do decide you need to demolish for some reason (replacing with a larger structure, making way for a highway bypass, etc), you can reclaim the materials. Try reclaiming the framing studs from your wood-frame house — doesn't work as well.
Stone: the choice for preserving the good ideas of the past and protecting the environment for the future!
I'm not sure you'll be able to do this
Metal and lumber aren't your competing materials. What you need to think about are bricks, breeze blocks and concrete as these are the materials that replaced stone in most of the world.
The problem with stone is the cost. First you have to find suitable stone, extract it, move it to where you need to build and shape it to the correct size. This last one is the killer, it required master craftsmen. These master craftsmen were the original freemasons, wealthy and free to move around the country in the way other non-nobles weren't. It's also incredibly heavy and massively labour intensive to lay even after being cut.
To maintain this as a viable building material you're going to need to solve these problems and especially solve them relative to the real competitor:
For most tasks these are perfect. Also known as cinder blocks or concrete masonry units, they are a fraction of the weight of an equivalent stone block, they're already perfectly shaped and designed for building. All you need is some cement and a brickie. Bricklayers are not master craftsmen, you can pick them up on a street corners as day labourers, just stop a van by the side of the road and wait. The blocks even have central hollows which help with insulation.
The only downside is that they're not exactly pretty, hence why, when looks are important they tend to be clad with an outer layer of:
Another small, artificial, lightweight, regularly shaped alternative to stone. Available in various colours, shapes and sizes, easy to cut when you need a half brick, usable for both decoration and structure. With all the advantages of breeze blocks except for size. They're relatively expensive and labour intensive to lay which is why they're not often used for large buildings any more.
Stone does retain one advantage over bricks and breeze blocks, that being damage resistance. This is where we come to:
This is the ultimate stone replacement. The kings of England were building with stone from the 11thC but the Romans used concrete. Nero's building code required concrete after Rome burned. The Pantheon might have granite columns at the front but it has a concrete dome. The castles are crumbling, the concrete still stands.
With these as your competitors the only option is looks. Natural stone will always look better.
Because it's cheap.
An advanced culture is as sensitive to available resources as an old-fashioned one. If stone is readily available and effective then there is little reason they would not use it for construction.
Tell the Czar that this method is cost-effective and will win favor with the environmentalists.
No usable trees
Imagine a land where there simply aren't any large woody plants to supply lumber for building. Maybe it's grassland with some shrubbery, or some fibrous flora that simply doesn't have the strength to be used as a primary building material.
Think of habitats like the Outer Hebrides—stone buildings are the norm there, as wood is very scarce.
If the location the culture lives in has little to no trees, then building with the few trees you do have wouldn't just be impractical, but foolish and idiotic.