Did they pay for your relocation expenses? If so, is there a clause in your employment contract to pay it back if you leave within a given period of time?
Do you want to stay in your new city?
If you are unhappy enough to leave, then why not bail up the manager who hired you, tell them point-blank that they lied to you and you know that the "round the corner" talk is just window dressing. Demand more money for your pain, etc. You should only do this if you are willing to get fired on the spot. But it is what I would do.
Immediately start looking for a new job. I would not put this one on my CV. Just mark the time as time-off to do a bit of travelling and relocating to your great new city and now that you have settled in, you are looking for work.
Don't worry about it being shitty legacy stuff. I have even worked on mainframe Cobol for a while and although I hated it, I ended up learning about a new industry and then getting a job with one of their competitors. Every silver lining has a cloud.