I will still call them space-ships unless you explicitly state that you are asking about giant floating balloons that do nothing but exist in space which wouldn't make an exciting story tbo. If you ask me, if the organism moves - it is a space-ship of some kind.
Forget natural food sources. Space is a giant void, in order to move in it you need some kind of repulsion and there is just no way that you can even reach the next body as a biological organism without simply losing too much water and burning too much energy (unless you want to go really slow and arrive someplace a billion years later). And then if you arrive at one of these bodies, well, your food source will be embedded in ice and rock that most likely just turning them into something of value for your organism consumes more energy than what you get out of it. Photosynthesis is also out of the question. I'm not saying you cannot harvest solar energy, but photosynthesis is extremely inefficient and not something you want for your living spaceship but rather for a tree that doesn't move.
So here are my suggestions:
First of all, unless you go into crazy sci-fi where the mind and the physical universe melt, stop having your organism move on its own. Not that you said anything like that, but I think it is implied. Give them inanimate engins like any space-ship would. Then they can use fuel like hydrogen or helium (which you will find a lot in a planetary system - basically on any gas giant) at the temperatures required for whatever process you desire. And do not feel bad about this, even today living humans are part machine for medical reasons - it should become much more common in the future. No more farting out to move, use a real engine is the motto here.
Second, your organism needs to be fed or have a super slow metabolism. A super slow metabolism is not the right answer since the advantages of a biological space-thing would be completely lost (unless you want "technically alive" - if so then state so). So just feed them. Check out the movie "The Matrix". They have a slime there that provides you with everything you need. I think the space-ship would eat such slime.
So you asked for the most likely food sources, I think they are fuel for the non-biological parts and "regular food" from planets for the rest. No sane civilization would build a comet-eating fart-ship that needs to drink water by the moon-load.