Weigh asphalt versus concrete. Concrete is more expensive, however, it's also more durable. When sealed properly, concrete can last for 20-plus years with minimal maintenance. While cheaper initially, asphalt requires sealing and yearly maintenance, which can add up over the course of its life span.
Consider patching your asphalt, not replacing or starting from scratch. If you currently have an asphalt driveway, you can cut costs by placing a new layer on top of the current one. This will temporarily expand the life of the driveway.
Do the paving of your driveway yourself. If you have the means and training to pave your driveway, save money and do it. But this is not the project to learn by trial and error because it may cost you more money if you make a mistake.
Cut the thickness of your driveway. Concrete driveways on average range from 4 to 6 inches thick. If concrete is the option you're choosing for your driveway, lean toward the four-inch thickness. For asphalt, opting to go on the thin side may shorten the life of the paving and may end up costing you more money in the long run.