Modern zoom lenses are pretty good, especially the newer and/or higher end (more expensive) ones.
What is your budget and what are your preferences in terms of quality vs cost. Also, was is your preference for size & weight? For example, two of the best zoom lenses would be the EF 24-70mm F2.8 L and the EF 70-200mm F2.8 L IS...but they are rather large and very heavy....probably not ideal for traveling, unless you are very dedicated to your photography while traveling.
Another thing to consider is whether you think you can get away with 'slower' lenses or if you will need or want 'faster' lenses.
We call a lens 'fast' when it has a larger maximum aperture...because that would allow you to get a faster shutter speed. Being able to use a faster shutter speeds can mean capturing motion better or getting adequate shots in lower light situation. A big advantage of prime lenses, is that they are often very fast. F1.8, F1.4 etc. Zoom lenses will rarely get lower than F2.8, and you will see that the top quality zoom lenses usually have a max aperture of F2.8 (for the whole zoom range). But that is what makes them big, heavy and expensive.
If that isn't a huge consideration for you, you might look at 'slower' zoom lenses....like the ones you have now. They might only have a max aperture of F3.5 to F5.6, but they are 1/2 the size and 1/4 the weight of the more expensive 'fast' lenses....which may be important when traveling.