I just recently shipped a large SUV from New York to San Juan. I got several quotes, and they all were in the neighborhood of $2,300. I shipped a Jeep down in 2019 for about $1,700.
The pickup process has improved because of COVID but can be confusing. In the past, you first went to the Port to get your car's paperwork, then to Hacienda in Old San Juan to pay the IVU, and back to the Port to pick up the car. You can now pay the IVU online. This is great, but you can't pay until you have the paperwork from the port, especially the port inspection paper and all your vehicle information, including the title. Here is my recommendation.
1. Bring your shipment papers, a tablet or laptop, and a phone with a hotspot to pay the IVU online at the port. You need to be able to receive emails on your phone or tablet. I did it on my cell phone, but it was really hard.
2. When you get the notice that your car has arrived, go to the port. There is an office in a trailer behind a lot of fences. It's there, but you have to search a bit. Ask directions if absolutely necessary (a guy thing).
3. There are two windows. One is the Port window, and one is for Hacienda for taxes, but Hacienda does not service customers. (More later). Pick up your paperwork at the Port window. They have posted the website for tax payments in the window.
4. Once you have the paperwork, you can complete the tax declaration and payment online. I recommend finding the site and starting the process before your arrival. There is a PR Government site for tax payments with many payment options. The car import tax page is on that site and is very specific. It takes some searching to find the correct page. The process on that page is lengthy, so a head start is a help. You put in make, model, VIN, shipping, and other data. Once at the port, you can fill in port inspection information and other items from the paperwork you got from the port.
5. When you finish the tax declaration, you will get the tax amount, and you can pay the tax via credit card online. They are then supposed to e-mail the receipt to you. When you get it, bring it back to the Port window, and they will give you a clearance paper. You bring the paper to the parking area, and they get your car.
6. My receipt never came by e-mail. After waiting a bit, going to lunch, coming back and, it had still not arrived. I went to the Hacienda window at the port; they looked it up and got me the receipt.
7. You then take your car to a regular inspection station - at many service stations, With no PR registration, you have to show them your title. Now you go to DMV.