An attempt to synthesise the various answers given, while giving some opinions of my own.
'Portable' is a bit of a vague requirement. Some instruments fit in your pocket. Some instruments fit in a small backpack. Some instruments fit in a large backpack.
I'm not sure what's too loud for a dorm room. It depends on your neighbour's patience. It depends how good you are (much more pleasant to hear someone good practising). It depends on how much you play and at what time of day/night.
The problem with inherently quiet instruments is that one day you may want to play to an audience, and having some volume would be desirable. But you can't have everything.
So with those things in mind:
Can be played with headphones, or an amp turned low.
Small keyboards are available. You'd probably find them limiting fairly quickly. MIDI flutes, guitars etc. exist but the affordable ones are essentially toys.
Can also be played with headphones, or an amp turned low.
Electric guitar is the obvious candidate. You can get travel guitars, but they're still in the large-backpack category.
Acoustic string instruments
A uke is a pretty good candidate. It's not pocket size, but it fits in a small bag. Cheap ukes are cheap. It's worth spending a touch more to get one with reliable intonation. If you get good, you can graduate to some really quite lovely instruments.
I'm mostly a guitar player, but I've been known to take a uke on business trips, so I have something to practise on in the hotel room.
The downside of most string instruments is that they're not all that robust. I wouldn't like to put a backpack containing a uke into a coach baggage trunk, or airport baggage handling.
Skills you learn on a uke are somewhat transferable to guitar.
There are other string instruments. Travel guitars. Violins.
Violins can get pretty loud, and sound awful when you're starting out.
More obscure: autoharp, strum stick, cigar box guitar
I'm not going to mention any brass instruments, because they're loud.
The smallest of the woodwind instruments are very small and pretty robust compared to string instruments.
At the cheapest end, there's tin whistles and recorders. For the sake of your neighbours, try and find an instrument with good intonation. Cheap recorders can sound dreadful. Flute, oboe, clarinet - getting progressively louder.
Some wind instruments come apart. Even a tenor recorder is pretty portable, since it separates into three robust pieces.
The lower the pitch of the instrument, the quieter it tends to be, since all the energy comes from your breath, and you have to move more air to make deeper notes. Smaller instruments might technically be quiet, but they can be shrill and the sound can carry.
Er, ocarinas are small and quiet, and surprisingly capable.
Melodica was mentioned, and seems fun.
Melodeons and accordions are designed to be loud. However concertinas are quiet and in the small-backback category.
A category just for the harmonica. It fits in your pocket. Your first one will be cheap. You will be welcomed by blues/rock guitarists. It's not quiet though. If you get into it, you'll probably end up buying more of them, in various keys.
Thumb piano, musical saw, etc.
These are fun, but perhaps odd choices as a primary instrument.