Want to move cities, what's the best procedure/order for moving, leaving this job, finding a new one?

I graduated earlier this year with an engineering degree, moved from my college city to hometown. Found a job 1.5 hours away (Toronto), so in mid-june I moved so I was about 5 minutes from my workplace. Since then the job prospects have not turned out well (company is rigid in how you advance, pay increases are minimal, mostly sitting/CAD work when I prefer a mix of computer/hands-on work). A higher-up also told me that in the past couple years, multiple people hired in my position have left because the company frequently ignores your requests and puts you where they want you, rather than where you want to work in the company. Also it's toronto, so I'm making almost no money, and by my math I won't have real savings going until 1-2 years from now.

I've decided to start looking for a job specifically in or around the city my uni was in, since I have the strongest roots there, not to mention rent is half, or lower, compared to toronto. I have some questions about the process:

-Should I put this job on my resume, since I've only been there for two months and it might look like I'm just job-hopping?
-How should I approach the subject of this job with future employers? I.e. Say its for financial reasons, not a good fit at the job, or both? Both are the main reasons I want to switch jobs.
-When I do find another job, what is a good way to avoid 'burning bridges' with this company, so what should I avoid saying?

Any advice you guys have is greatly appreciated and thanks in advance!

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