Since I overwhelmingly prefer to vacation in warmer weather, shorts are a key part of my daily wardrobe. My favorite travel shorts are these:
Patagonia Stretch Wavefarer Walk Shorts

These shorts are a recent addition to my bag, and They. Are. Awesome.
They’re comfortable, they look good, and they dry quickly. All boxes checked.
I usually travel with two of these so I can have a pair to wear while the other is being washed and dried. The shorts have two roomy pockets up front, two in the back, and a couple of buttons that function to keep the fly closed. The material has a small bit of stretchiness to it which helps with comfort. There’s a drawstring present around the waist, and I’m honestly not sure what the purpose of this is. I just ignore it, but if it bothers you you can simply take it off.
Patagonia makes a non-stretch version of the Wavefarer Walk Shorts as well [as of mid-2018, these are no longer available. The stretch shorts are still around]. I own a pair of these, and between the two models, I strongly prefer the Stretch version. They’re just more comfortable, and there’s more room in the crotch.
In addition to these excellent shorts, I also have 2 older pairs of North Face Paramount Peak convertible pants (the style where the leg portion under your knee zips on and off) that I sometimes use as travel shorts. I don’t like the leg extensions, so I leave those off and use them purely as shorts. This is a good product, but there are two problems.
1) They’re made of a thicker material and thus take longer to dry
2) The product quality has allegedly declined over the years
The ones I own are the original Paramount Peaks that are many years old and long discontinued, and one trend I noticed reading user reviews of the newer iterations of these pants is that they are not nearly as good as the older models. The pockets are different, and many people complain about the sizing. Since I found the Patagonia shorts, which in my opinion is a better product anyway, I haven’t bothered trying any of the newer North Face ones.
As with all my personal recommendations, please make sure you actually try these on in a store before buying. You may find something else that is similar but fits you better. And that’s what’s the most important; that you buy something that works the best for YOU and will make your light travels more pleasant.