Cement or concrete roads
1. The first thing you might have to do, if the technology is not yet available in your campaign, is find out how to make cement. Cement is actually made by adding water to limestone in the appropriate measures. The water releases gases in the limestone that cause a chemical reaction. The result is a breakdown of the rock and the creation of heat. With the right mix, you get a paste that hardens when dried: cement. If you add volcanic ash to the cement, you actually get concrete, which is more durable and will resist the effects of weather for a longer lasting road. Perhaps a visit to an alchemist of renown will provide you with the proper recipe for concrete.
2. Next, you'll need quarrymen to mine for limestone and gather the volcanic ash. While the labor is intense, it does not require a lot of skill, but it will take quite a bit of time to lay down 170 miles worth of road. Without the benefit of cement mixers and gas powered engines, you'll need several hundred workers to mine the stone and lay the concrete. If you had 500 laboroers, you might be able to lay down 30 miles worth of road in a year, so 170 miles would take roughly five and a half years. Without the DMG handy, I can't tell you how much the annual cost per unskilled laborer is, but perhaps someone else can provide that. (If this road is going to lead to another country or countries, you might also consider asking each country to pick up its share of the tab)
3. You will also need to hire some engineers who are capable of surveying the land and making sure the road follows the best course. You can probably count on needing five engineers for the task.
4. While the pouring of concrete is not something that requires stonecutting, a stone mason with a trained eye would be beneficial for overseeing the pouring of concrete in the right dimensions, and making sure the road is level. Again, a team of five will probably do you well for this. I'd recommend dwarves, since they have the natural ability of detecting changes in the grade of a slope. You might be able to buy them off for half their normal cost along with the "secret" of how to make concrete.
5. Next, you have to figure out how to pay for this massive project. It is of course a public work, and therefore it is entirely appropriate to use public funds. You may want to consider a one time property tax increase or a bond to pay for the road. This may gain the disfavor of property owners, but, if you promise to give future tax breaks to the property owners to pay them back, it may lessen their opposition. Be sure though to collect enough excess from the one-time tax so that you have some money to place in an interest bearing account. (if you have a bank in your domain) The interest you receive annually from this account would be used to pay for the future maintenance of the road.
6. You'll also probably want to construct way stations on the road and small troop garrisons to protect travellers. To pay for this, consider the idea of making the road a toll road. By doing so, you can generate the revenue necessary to pay for troops, but you will also be able to place the revenue burden on travellers; many of whom will be travelling to your domain from other parts of your campaign world. Thus, this extra tax is not something that will have a large impact on the purses of your constituents.
7. Offer property tax incentives to entrepenuers who can build inns, taverns and stores along the road. You'll charge them a small tax for sure, but by giving business owners a tax incentive, they will build their stores along the road. By having these available, more visitors will be likely to travel your road, thus increasing revenues from the toll. In addition, it may help build a substantial trade route that will allow your domain to flourish. If it does well over the first 20 years or so, you may decide to build new roads to other kingdoms. (Those dwarves, to whom you previously gave the technology of concrete, might make good trade partners to start)
8. The other advantage to building the road is the fact that you will be able to provide jobs to many people. As long as they have an income, they are more likely to be happy. So, consider the fact that the road is merely an investment. The more people you can hire to do the job, the greater your investment and the sooner the job will be accomplished.
To sum it up, you will need:
1. To pay an alchemist for the recipe for concrete
2. Hire an army of 500 unskilled laborers
3. Hire 5 engineers (skilled laborers)
4. Hire 5 stonemasons (skilled laborers)
5. Eventually hire additional milita or soldiers to guard the road
6. You may also need to hire an administrator to oversee the entire project.
You'll have to look up what the cost of each of these are.