If you are committed to maintaining purity, then it would be good for you to reflect on 1 Thessalonians 4:3-6 before deciding whether to vacation together and consider whether this could be a situation in which you will be tempted and not able to control yourself:

It is God’s will that you should be sanctified:  that you should avoid sexual immorality; that each of you should learn to control his own body in a way that is holy and honorable, not in passionate lust like the heathen, who do not know God; and that in this matter no one should wrong his brother or take advantage of him. 

Another important point to consider is how your actions will be perceived by others.  If someone you know—say a younger brother or sister in Christ—hears that you have vacationed alone with another unmarried person of the opposite sex, what will they think?  (And quite honestly, what would you think?)

In today’s day and age, it is automatically assumed that you will be sharing a hotel room and are sleeping together—even if you are not.  Perception is reality.  So could this interpretation cause someone to become confused and reject Christianity because of your example?  It’s something to think about.  As a believer, you are ultimately held responsible for your actions and how they impact others.

Ponder “The Believer’s Freedom” passage in 1 Corinthians 10:23-33:

“Everything is permissible”—but not everything is beneficial.  Everything is permissible”—but not everything is constructive.  Nobody should seek his own good, but the good of others.  Eat anything sold in the meat market without raising questions of conscience, for, “The earth is the Lord’s, and everything in it.”  If some unbeliever invites you to a meal and you want to go, eat whatever is put before you without raising questions of conscience.  But if anyone says to you, “This has been offered in sacrifice,” then do not eat it, both for the sake of the man who told you and for conscience’ sake—the other man’s conscience, I mean, not yours.  For why should my freedom, be judged by another’s conscience”  If I take part in the meal with thankfulness, why am I denounced because of something I thank God for?  So whether you eat or drink or whatever you do, do it all for the glory of God.  Do not cause anyone to stumble, whether Jews, Greeks or the church of God—even as I try to please everybody in every way.  For I am not seeking my own good but the good of many, so that they may be saved.

Before you make your final decision of whether or not to vacation together, may I advise you to please spend some considerable time in prayer. 

There is a way that seems right to a man, but in the end it leads to death (Proverbs 14:12).

Man looks at the outward appearance, but the LORD looks at the heart (1 Samuel 16:17).

Ask God to search your heart and reveal anything that is not clean or pure  or glorifying to him (Psalms 51).  Know that he has given us his Word to help us and for our own good (even though it may just seem like rules, rules, rules!).  Like a good parent, our heavenly Father loves us and has set up perimeters to protect us and to keep us from falling into harmful and hurtful life stiuations.