I can see musical instruments being very good for morale during a bugging-in situation and for that any instrument you can play or wish to learn will be a good thing -- be it a piano, cello, guitar or a set of drums. An alto sax has a nice tone and I tend toward jazz... Good entertainment & just a good way to pass time and keep your mind occupied.
In a bugging-out situation, the instrument naturally needs to be portable and needs to take a subordinate role to other stuff that needs to be carried. A harmonica fills the role, as does the small soprano recorder (common flute) we played in the 4th grade. I have an alto recorder that I need to learn -- it's actually a nice instrument for which I have a lot of classical sheet music. A harmonica is even smaller and possibly easier to learn to a point; to become really good takes time and lots of it -- start now. $.02
The harmonica does require a fair amount of practice to become proficient with. For snorts and giggles, I've made a list of instruments that can be stuck inside of pack or pocket without taking up too much room and are tough enough for the road:
1) Harmonica - takes a lot of practice to become good enough to want to listen to, and relatively vulnerable to contamination. Diminutive size and ability to solo makes it a classic travel companion. Buy a hard case to protect it. Expect to pay $25-$50 for a decent harp.
2) Various western flutes (Ocarina, Recorder, Tin whistle, Fife, Tambor, etc). They tend to have simple construction, are relatively compact, and often available in polycarbonate or other robust materials. Mountain Ocarinas makes a couple of indestructible models with an octave and a major 3rd chromatic range. Usually lines up with western semi tones. I'm leaving orchestral instruments out due to complicated linkages and a general intolerance to adverse weather.
3) Various aboriginal (Native American, Japanese Shakuhachi, Peruvian Quena, etc) flutes. Probably the most melodic sounding, but notes don't necessarily correspond to Western tones. Try not to say "I am Kane, I will help you"
4) Mbira (African thumb piano) - Often found more as a storytellers companion then as a stand alone musical instrument. If you're a good storyteller, expect to be invited over every time there's a power outage.
5) Jaw Harps and Kazoos - snorts and giggles. Nothing really left to say
6) Drum pads and sticks / spoons - Great way to keep yourself amused. Maybe not so much for an audience, unless you have some awesome cadences (i.e. Drumline 2002).