If I was arrested for the first time ever while I was on vacation out of state, is there any way to have my arraignment without my being present?

Some states allow "Written Pleas of Not Guilty".  Usually, attorney's file "Written Pleas of Not Guilty" and ask that the matter be set for a pre-trial.

Without an attorney, you are going to have to call the court and see if they accept "Written Pleas of Not Guilty" by a pro se defendant.

From time to time I have had success with filing motion to allow defendant's to appear telephonically.  The court usually allows this in matters such as arraignments and pre-trials.

Of course, you could hire or ask the court to appoint an attorney for you.  In that case the attorney can file a "Motion to Exclude You from the proceedings". Attorney's do this all the time for people that reside out of state.

If the court grants the motion to exclude you from the proceedings the entire matter can be resolved by your attorney, without you ever coming back to court.

Hope this helps