First, let's look at a definition of stress:
Stress is a feeling of emotional or physical tension. It can come from any event or thought that makes you feel frustrated, angry, or nervous.
Stress is your body's reaction to a challenge or demand. In short bursts, stress can be positive, such as when it helps you avoid danger or meet a deadline. But when stress lasts for a long time, it may harm your health.
So, it is a reaction to a challenge or demand that results in tension.
"My question, then, is this: if stress is caused by change to normal routine, would a good change with only positive effects still be considered stress? For example, going on vacation. The travel could certainly be stressful (or perhaps just anxious), but once a person arrives, lets assume they have a very good, relaxing stay. Could this be considered a stress since it is a change from the normal routine, despite having no negative effects?"
According to the above definition, though the trip there may be stressful, for a normal person, the stay itself will likely not be considered "stress." However, this depends largely on the psychology of the person involved. For example, if someone has serious anxiety when breaking from routine, such a person would be more likely to find a vacation stressful, even the part of it that is supposed to be relaxing and enjoyable.
Stress is often presented by the healthcare system as a negative thing, however, the fight or flight response is something which allowed us to be more capable of survival in difficult situations, historically speaking. There are certain doctors/researchers who embrace this more positive outlook, attempting to see the possible positive aspects of stress, rather than viewing it as only a negative thing. This is useful because the mere act of viewing stress as only a negative thing can actually compound the amount of stress felt, as one is not only stressed, but becomes stressed about their stress. Here is some information and a TED talk by Kelly McGonigal who covers the idea of stress from that standpoint: http://www.ted.com/speakers/kelly_mcgonigal She also wrote a book called "The Upside of Stress" if you're interested. I've listened to part of the audiobook of it and it's quite good.