1. PLAN AHEAD. You know where you are going. Even if you are going to book a guided tour, you can easily find out what sights you are likely to see. So use the internet and travel guide books to see what there is in the area and even work out the best spot to obtain that postcard shot. With the internet you can even plan you day and route by sequencing what you want to see and how long you want to spend at each sight.e.g. VISITACITY.COM. Print out your itinerary and bring it with you. Even if you don't stick to it, it will serve as a guide.
2. AVOID THE CROWDS. If you are on your own this is easy, simply get up earlier or stay later. If you are with a group, either walk ahead of the group so you are first at a sight, or lag behind and take a shot when the group has moved on. However the latter poses the risk of getting lost in a crowded Asian market or temple!
3. USE TIME WISELY. Usually in a group the guide gives you a specific set period before you return to the coach. Don't follow the crowd. Find a quieter spot and photograph the less obvious. If you photograph the Eiffel Tower from a distance it looks like any other photo, so why not shoot it from below or as a reflection in a puddle of water or a car mirror? Different but still the Eiffel Tower.
4. BE CREATIVE. Use reflections. Shot from a different angle, either from ground level or up on a high building. Use a very wide lens or maybe a long telephoto. Shoot details rather than the whole scene. Photograph people photographing the scene, etc.
5. CAPTURE THE FLAVOUR or MOOD. You don't always have to shoot the major sights. Photograph local food or crafts, signs or shops or architecture or people (especially in local dress) to capture the flavour of a place.
6. TALK TO LOCALS. This is easily overlooked. Local people know the best spots, the little hidden gems, the quiet cafes away from the expensive tourist spots and how to get there! Ask in your hotel or shopkeepers, or even people in the street. Most people are happy to help a stranger.
7. ALWAYS HAVE EITHER A CAMERA or a PHONE. You never know what is out there, even if you are just going for a sandwich or lunch or an evening stroll. Bring a camera or your smart phone because when the unexpected happens you will wish you had brought your camera! Also pre-download maps of the area onto your phone, so if you do get lost, it will probably help.
I hope this helps you take better travel photos!