As in any community I would say stick with the crowds and avoid dark alleys at night. There is a lot of night life in Waikiki and people are walking around all hours. As other people have stated, it's best to check out an area in the daytime. On the whole I believe Honolulu is considered fairly "safe" compared to other major cities.
The web address below is for a crime map from the Honolulu Police Department website which will provide you with some current statistics on different areas of the island. I hope this helps.
The areas around Waikiki (Kapahulu, Kapiolani, Ala Moana, Kaimuki, Mc Cully...) are generally considered "safe", but I would recommend that you visit those during daytime and stick to the commercial areas. As with any large city, you do not want to be a tourist wandering deserted streets at night! Aloha!
Waikiki is a very safe area, my husband and I go to Waikiki several times a week during the daytime and nighttime and always have a great time. There are a few places on Oahu that you might want to avoid during the nighttime hours but Waikiki is definitely not one of them. Have fun and enjoy Waikiki!