Brass players can practice using just their mouthpieces, and drummers can practice with just sticks. What can a guitar (or similar instrument) player do to practice when they can't bring along their instrument?

It depends on what exactly you want to practice. I feel like I've answered this before so it may be a dup.

1. If you are a musician you can always practice your craft by singing. It may sound off topic but it really is not. The ability to sing, and process short melodies in your head is critical to playing any instrument. So, no guitar? Practice music rather than chops.




2. Get your hands of a small travel guitar. I have a Martin Backpacker that I love. I take it on trips, and pretty much everywhere. If I know I will not be able to rehearse for a while on my main set up this is a good substitute. They make other practice devices that are just a small finger board and strings. It keeps you active.




3. Along the same lines, if you are traveling for work or vacation scope out musics stores in the area. You can walk in and jam for a while on floor models. Most stores don't mind and you may be youtube exposure.




4. In the worst case scenario where you can't do anything you can try some finger dexterity exercises taping out patterns on the table top. This will at least keep your fingers nimble.

There is quite a bit you can do, even if all you have with you is your mind.

Visualization/Memorization

Memorize the fretboard by visualizing it in your mind. You know, of course, how your strings are tuned. Using that, visualize (for example) where every G is on the fretboard. See the fretboard markers in your mind as you do this. This works well with flash cards: You write out all 12 chromatic notes on flash cards, and then as you draw each card, you see in your mind where those notes are.

Similarly, memorize where each chord is on the neck. For example, where is every G? As with individual notes, visualize the fretboard markers--see the fretboard in your mind.

Memorize the circle of 4ths/5ths. This is not specific to guitar, but very useful for any instrument.

Ear training

Practice ear training. There are many ear training courses that are audio-only; these are perfect for listening to while you are driving, or any other time you want. There are also many ear training apps you can run on your phone. This is a good way to use time away from your instrument.

Guitar substitute

Google for "guitar practice neck" and you will see guitar necks, with or without strings, that are meant for practicing fingering. These are pretty inexpensive and small, and might be an alternative to your real instrument.

Not much I’m afriad. Unless you’re willing to DIY a quick fretboard out of card and a pen, you’re pretty much limited to practicing theory - how to change a chord to make it extended, how to play a Lydian scale compared to aeolian. Practicing strumming rhythms could also be possible.