Ive taken the LSAT 3 times (two 154's and a cancel) but never really felt like i put the time in i needed to succeed on it. I got into a few schools this cycle but no where i really wanted to go. I am currently living at home and am working at a law firm but dont really want to be living at home anymore. That being said...
would my work experience look worse if i change firms (and cities) by appearing to law schools as a "job hopper" and not really demonstrating growth and experience and thus not help me in the application process, or would switching cities and continuing to work at another law firm still look the same as sucking it up and staying here/working at the same firm for another year?

As far as getting into law school goes, it doesn't matter.
Besides, most young people have a number of shorter term jobs.

The only thing im worried about is what if my LSAT score doesn't go up as much as i would like (last practice before the most recent LSAT i took i got a 162 and still felt i could have done better, regardless even a 160 is way different than a 154). Then would firm hopping before law school not look as good as staying with one firm and gaining experience there if my LSAT doesnt go up that much?

also this was my first year out of undergrad, so im worried i wont look committed to a job which will turn another year off into a waste of time if the law schools i apply to dont like my job switching/would rather me stay at the same firm for two years without a significant increase in LSAT score.

I can't really see commitment to a job being that big of an issue when you're leaving the job(s) to go to law school. I'm sure you'll be fine switching, but try to leave on good terms with your current job (don't just not show up one day). Plus if you switch jobs soon, you'll have roughly 9 months to a full year with the new place (assuming you're applying in the fall).

I worked at one firm for a year & 3 months, and then moved on to another, where I worked for about 5 months before submitting applications. I don't feel like it negatively impacted my applications at all.