私は私のまちにやすめから、「name of town」がすきです.
I like my hometown because I can relax here.
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くつろげるから「name of town」がすきです.
くつろぐことができるから「name of town」がすきです.
sounds right to my ears.
休むことができるから seems more like "because I can take a rest" or "because I don't have to go to work here."
As for the usage of "から" itself, your sentence was correct.
休むことができるから would compensate the translation better i think.