Under 18 U.S.C. § 2423, transporting a minor across state lines is a crime when done with the purpose to engage in illegal sex or child pornography:
(a) Transportation with intent to engage in criminal sexual activity. --A person who knowingly transports an individual who has not attained the age of 18 years in interstate or foreign commerce, or in any commonwealth, territory or possession of the United States, with intent that the individual engage in prostitution, or in any sexual activity for which any person can be charged with a criminal offense, shall be fined under this title and imprisoned not less than 10 years or for life.
(b) Travel with intent to engage in illicit sexual conduct. --A person who travels in interstate commerce or travels into the United States, or a United States citizen or an alien admitted for permanent residence in the United States who travels in foreign commerce, for the purpose of engaging in any illicit sexual conduct with another person shall be fined under this title or imprisoned not more than 30 years, or both.
(c) Engaging in illicit sexual conduct in foreign places. --Any United States citizen or alien admitted for permanent residence who travels in foreign commerce or resides, either temporarily or permanently, in a foreign country, and engages in any illicit sexual conduct with another person shall be fined under this title or imprisoned not more than 30 years, or both.
I can't find anything suggesting that the intent to obtain an abortion would implicate this or any other law, though there have been attempts, such as the perennially introduced, but never-passed Child Interstate Abortion Notification Act.
