You're asking things here that it takes a thorough consideration of your entire financial situation to answer. The general answer is that the trustee assigned to your case would get all of your assets (for the benefit of your creditors) that are not specified in your filing as "exempt" under your state's laws. Exemptions are a very important subject in bankruptcy and a mistake there can lose assets you want to keep. I strongly recommend that you consult with and retain a qualified bankruptcy attorney in your area.
If you read through the questions that are posted in this category, you will see many examples of people trying to represent themselves in Bankruptcy & running into problems, problems that many times cost them far more than the modest fees most bankruptcy attorneys charge.
Once a bankruptcy is filed, many times these problems cannot be fixed and you must just live with the consequences.
Some people can learn from the mistakes of others, most people have to learn the hard way! Hope this perspective helps!
I have to agree with the first two answers. You need an experienced attorney to take you through the exemptions (and to obtain proof of value). In January New York adopted a new scheme of exemptions for debtors, and you can elect between a specific set of State exemptions, or you can elect exemptions under the Federal set. Given the cars' value, you really need to discuss this with a local bankruptcy attorney.
I assume that when you mean "file by myself," you mean file just you and not as a couple. Since your name is on both cars, you may have to decide which car to give up. You'll only get one vehicle exemption on one car. Of course, you can always buy the other one from the trustee so you can keep it. But you also have a wildcard exemption that you can use on either vehicle.
If you file as a couple, you may be entitled to a vehicle exemption on both cars. It is probably worth hiring an attorney to work this out and make sure you get the biggest exemption bang for your buck. Good luck.