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She likes Nara all the more because she can feel relaxed there.
Literal
She [topic-は] relaxed [attributive] feeling [become-can-なれる] [because-ので] all-the-more Nara [subject-が] like.
A nicely layered explanatory sentence. くつろいだ ('relaxed') is the past form of くつろぐ functioning attributively — modifying 気分 ('feeling, mood'). ~気分になる ('come to feel X') is the standard pattern for entering a mental state, and なれる is the potential form of なる ('become, get'), giving 'can come to feel relaxed.' ~ので ('because') links the reason to the result, sounding softer and more indirect than ~から. いっそう ('all the more, even more') intensifies a feeling or evaluation in a comparative sense — she likes Nara not just plainly but additionally so. Nara, Japan's first permanent capital (710–784), is famous for its great wooden temples and the free-roaming sika deer of 奈良公園 — a quiet, atmospheric place that lives up to the relaxation cited here.