3. Do you prefer that we spend all our time together, or are you comfortable with us separating to do our own thing every once and awhile?
To me, this is the most important question. I enjoy doing things when I travel that not everyone likes to do — I'll hike to the top of a mountain on a sweltering hot day just to catch a glimpse of an ancient library located at the top or spend hours wandering through an art gallery. And I want to be able to do those things without having to worry that the person I am with is enjoying themselves too.
Sometimes the easiest thing to do is to split up for a day, an afternoon, or even just a few hours, so that you can both have an experience that the other person wouldn't enjoy. But, you need to know that your travel buddy is up for that and that there will be no hard feelings either way.
4. What type of accommodation are you picturing? Hostels? Campgrounds? B&Bs? Hotels?
Not only the type of accommodation, but the area of the city you are wanting to stay in is also important. (Prices tend to get higher the closer to the centre of a city you get — though that's not always true if you are willing to stay in hostels).
Are you both okay with the co-ed room in a hostel dorm? Are you looking for a room for two at a B&B? Or, are you both wanting your own room at a hotel? Make sure you know where you are both expecting to lay your head before packing your bags!
5. What activities or attractions are an absolute must-see for you and what are you flexible about?
You are headed to New York and you will give a limb to get to the top of the Empire State Building — even if you have to stand in line for the entire day.
Your travel buddy needs to know that, because if that isn't on their to-do list, this could lead to an argument. When I am headed on a trip, I always let my travel buddy know what my must-do things are and if hers/his matches up then we do them together. If not, see #3 above.