The thing to remember about travel shoes in general is that you are going to focus on comfort rather than looks and you want a shoe that will provide protection so you can go everywhere without a problem. Some folks recommend you skip taking sandals or even flip flops as neither one offers protection but I always have a pair of sandals with me. I have taken flip flops on occasion when I was staying at a place like a hostel where I was sharing facilities with others.
In general, the type of shoe you take will depend on where you are going and the season you are doing in. For instance, if you are mostly in towns with hard sidewalks, roads, or public walkways you share with bicycles, you will want a sneaker or running shoe. You don't have to get the most expensive ones, just know you will be racking up distance if you are walking all over.
On the other hand, if you are doing a lot of walking along trails or terrain that is a bit more rugged, you might want to look at a light hikers or trail runners because they are sturdy, protective, and are made for long excursions. In additions, most of these shoes are designed to be water resistant so they are great for wetter weather. If you won't be doing a lot of hiking, you might not bring a pair like this with you.
If you need a shoe for dressier events, you might want to focus on shoes that are more comfortable rather than being fashionable. This type of shoe might be similar to one you'd wear if you had a job where you have to be on your feet most of the day. It doesn't have to look great, it just has to do the job.
To see if the shoe is going to work, you will have to do more than just put them on and walk a few steps around the store. You should first pick up the shoe so you have one hand around the heel and one under the toe. You need to bend the toe upwards. You are looking to make sure the shoe bends under the ball of the foot. Then twist the heel and toe to see if the sole feels like a wet noodle or if there is a bit of resistance. You want a shoe that has a bit of resistance.
If you can, walk down an incline to see how the shoes feel and react. Make sure your toes are not touching the front of the shoe, if they do, look at a different pair. Then walk up some stairs to see how they work. You want to make sure that your heels are not lifting in the shoe more than one-eighth of an inch otherwise you have the possibility of developing blisters.
The last thing to keep in mind is that you do not want to skimp on cost. If the shoe you like is on sale, great but don't settle for a cheaper pair of shoes due to cost. Most of the time when you are traveling, you are going to be walking around and you need to take good care of your feet. Spend the money because you are investing in yourself and your trip. You don't want to be sidelined due to hurting your feet.
If you end up bringing a light pair of shoes and heavier boots, then pack the lighter pair and wear the heavier shoes to save weight in your suitcase. I usually wear the heavier one and slide the lighter pair in my backpack where I have a specific pocket for shoes. Let me know what you think, I'd love to hear. Have a great day.