Is it permissible to perform tayammum for Fajr prayer while traveling for someone who cannot find a suitable place for ablution and prayer, and is there sin upon one who misses the prayer due to not finding a suitable place to perform it?

If water is available, the absence of a designated place for ablution (wudu') or prayer does not permit tayammum (definition) (dry ablution) or delaying the prayer. One must perform ablution and pray on time; for the entire earth is pure and a mosque, as the Prophet, peace and blessings be upon him, said: "The earth has been made for me a mosque and a means of purification, so wherever a man from my Ummah is, and the time for prayer comes, he should pray." If water is not available or its use would cause harm, then tayammum is permissible, but it is not permissible to delay the prayer beyond its prescribed time. If one falls short in performing the prayer on time with purity, she is sinful and must repent.