It is not the big problem you may think. An experienced matrimonial attorney can easily handle this case. The solution is service by publication. To properly answer your questions and address your concerns, the best way to handle this is by retaining an experienced matrimonial attorney. Use 's Find a Lawyer tool to select a qualified attorney. Good luck.
First you should exhaust all resources on trying to locate her through mutual friends, family members, and internet/social media. There are other avenues to obtain constructive service if you are not able to obtain personal service. You can have the local sheriff attempt to serve her a copy of the divorce complaint at her last known address, or send certified mail with return receipt. If unsuccessful, you can publish a non-resident notice in the newspaper that would give notice for four weeks that a divorce has been filed against her and she would have a month to respond. This should be sufficient for constructive service of process. You can set a final date and appear with two witnesses that can affirm that the testimony you are giving is true and correct and they believe you to be an honest person. I advise you to hire an attorney to assist you with this.
If your try to find her and can't, you can petition the Court to serve her by publication (publish in a newspaper). If the Court allows you to serve your wife by publication and she does not respond, you can then ask the Court to grant you a default judgment for divorce.
I suggest you contact an attorney and ask what they would charge for this case. It seems that it is an easy case and the attorney would not have much work to do. With the help of an attorney, you should not have a problem getting divorced, with or without knowing where your wife lives.