The custom nowadays is that a boy and girl go on shidduch dates to see if they are for eachother. Halachically speaking would a boy be allowed to go on a date if he is worried that he will excessively gaze at her and have inappropriate thoughts?
1) Regarding a shidduch, the Shulchan Aruch says, "For the sake of marriage, a man may view an unmarried girl or lady to see whether he likes her appearance and general characteristics. It is not only permitted; it is advisable and correct to do so."
2) If you're worried about inappropriate thoughts, the Gemara states, "Inappropriate thoughts are one of three things that, on a regular basis, a person is not saved from."
Still ask your Rav for guidance on how to overcome this issue.
3) Do not avoid going out. For the Gemara tells us, "One who delays marriage, will each day of his days in sin." Meaning, an unmarried man will lack the permissible outlet for the passions inherent in man's nature and will come to entertain licentious thoughts regularly.