I'm guessing your dad lives in Louisianna, and his house is also located there, but as stated previously I'm also unsure if I'm perceiving that right, but i digress. I also don't know your relationships with your dad and your now ex-girlfriend(i.e. you have a love/hate your pops, or you're ex and you have a love/hate relationship as well.) Regardless both of these examples are unhealthy, so that is the case thats's a seperate answer that won't be answered here until more clarity is brought to your post. I figured you posted it drunk for a reason, you wanted to blow off some steam and/or find opinions/perspectives to bring these current conflicts in your life to a resolve so if that is the case feel free to answer it here, p.m., or text me, but once again i digress: If you are seriously done with your girlfriend and she's kicking you out, and this currently theoretical house( to me at this time) is in Lousiana and due to your relationship to your father being unknown, From a rational, standpoint i say get the fuck out of Upstate NY cause you're gonna freeze your ass off and get down to LA to be with your father. But from an emotional/rational(the emotional heavier more so probably) standpoint You'll "kill two birds with one stone" by fulfilling one of your goals(traveling, as we almost became roaddogs before) as well as support your Dad in his time of need. It will be hard to do especially if you don't have the best relationship with your father, or if he gets himself into situations like this all the time(these things i dont know, but highly doubt due to the fact he's not losing a room in a apartment, or even his own apartment but a whole house.) but i feel you mentioned him because you care so that is probably what you should do to be "healthy" in "soceity". You also could just run, but most people who run don't ever get to where they're trying to go due to emotional factors, and you seem like this latter approach would not be "beneficial" at this time. I hope i helped answer some questions in your mind, or at least aided you in becoming more "comfortable"/accepting of the situation at hand. Like i said P.M., reply to this, or shoot me a text man, whichever you feel comfortable with, or don't at all if you feel you don't want to. I give you this advice because I realize i should follow this advice more often myself, but by giving you advice I am therefore helping myself, and in all honestly it makes me feel better, therefore it is "selfish".
Once again hope I helped man, be easy, and be safe
Peace.