When testing a violin you need to look for sound, playability and responsiveness, and budget. Get someone else to play the instrument for you. Listen to the sound. Even if you don't feel like you know what you're looking for, you can still listen really closely to the sound and just say with your gut instinct whether or not you like it.
Do a blind test. It's really useful if you play violins to someone without them looking, and get them to write down exactly what they think of each example (Exhibit A, Exhibit B, Exhibit C and so on). As you do this, think about how each violin feels under your fingers. Make sure that you make a note of the same instruments again, without saying which one is which. Then swap around.
Have the person the other person play the violins back to you whilst you listen without looking. Ask *them* to make a note of which ones they enjoyed the playability of as well. This way you're likely to get a very clear and well focused answer that you can believe without prejudicing yourself in any way.
When you're testing violins do remember to check for wolf notes, and also remember that the sound under the ear and the sound that you hear on the other side of the room can be very different. So make sure that when you're getting somebody to play the instrument to you that you're doing so from a distance not just close up.