So, borders as we would think of them - that being a clearly demarcated, fortified line with manned checkpoints through which one must pass - did not exist, and neither did formal immigration systems. The state apparatus for maintaining them just wasn't there. You did have marches, such as on the English-Scots border, which were basically more-or-less militarized frontier zones, but the marcher lords were concerned with invading armies and raiding parties, not individual travelers. You might well be made to pay a toll for crossing bridges, and there were customs men in the ports laying fees on merchants importing goods.

Furthermore what would the journey actually be like to cross Europe in the late middle ages? Would it be radically different for a nobleman than for a peasant?

I'm really not prepared to speculate as to what a typical journey would be like; there are too many variables involved. Certainly, your journey would probably be a bit more comfortable and secure as a noble than as a peasant, as you would likely have servants and/or armed followers with you, and you would probably be mounted. As to your original hypothetical, I would find it odd for a nobleman to take such a long and circuitous route; long distance travel for leisure was rare. It's much more likely that he takes ship somewhere like Bilbao or Corona, disembarks at a north German port, and proceeds to Bohemia from there.