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Traveling:[1]
One is obligated to put on Tefillin even during travel and he hence must either bring his Tefillin with him, or is to borrow from another. He is not to travel to an area if he will not be able to put Tefillin on there.
Not to travel without Tefillin:[2]
Some are accustomed not to travel from home without bringing their Tefillin with them. This applies even if they plan on returning that day, as they fear that perhaps they met get stuck in travel and do not want to rely on borrowing Tefillin from others.
[1] Piskeiy Teshuvos 25:5
How far must one travel to fulfill the Mitzvah of Tefillin? See Ashel Avraham of Butchach 25
[2] See M”B 110:20; Piskeiy Teshuvos 25:5