Hi. I think it depends on what you're trying to say. If after travelling across the desert you're going back to "university" to attend classes (go there as a university student who studies there), then you must say: "go to university" but if you're considering "university" as a physical place that you need to go to (much like the supermarket or the cinema), then you should say: "go to THE university"

Both sentences are incorrect. The simple reason being that "travel" should be used as "travelling/traveling" depending on whether you prefer the American way of writing it or the British way. Since your sentence begins as "We'll/We will + be" requires the word "travel" to change to "travelling/traveling"