Clicking on front right handside wheel

Most likely cause is a binding upper strut mount. Reach over the top of the tire and loosely wrap your fingertips around the coil spring, then have a helper slowly turn the steering wheel. The spring should turn smoothly with the wheel and tire. If it winds up, then snaps free and turns, the upper mount is binding.

There's too many variables to know the cost. I don't know the shop's hourly labor rate or the quality and brand name of the parts they would use. The easiest cars to work on are older Chrysler products. I can change a strut or a strut mount on one side in about 20 minutes. Most cars take a lot longer.

First the mechanic will inspect the steering and suspension components to identify any other worn parts, then he will verify a strut mount is binding. Replacement of a mount requires removal and disassembly of the entire strut so it is common to wait until the struts also need to be replaced. That is a fairly common job.

There are other ways a strut mount can fail that can not be easily determined until they are removed and inspected during the strut replacement procedure. At that point the mechanic has to tell you more parts are needed than what was expected. They hate doing that. Instead, some shops will quote you a repair estimate that already includes those mounts in case they are needed, then they surprise you with a lower bill if they find out they are not needed. The drawback is their estimate is higher than the second opinion you got from another shop so they might not get your business. It's important to compare different estimates to see that they are including the same parts and services.