まんざら〜でもない
not altogether (bad), rather pleased
まんざら + でもない / 〜ではない / 悪くない
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まんざら comes with a negative and means "not altogether, not entirely": 田舎暮らしもまんざら悪くない, "country life isn't so bad after all".
The set phrase まんざらでもない describes someone who is quietly pleased while pretending not to be: 褒められて、彼はまんざらでもない様子だった, "he looked rather pleased at the praise". This is its most common use, and it's a lovely, very Japanese piece of understatement.
It's close to あながち〜ない, "not necessarily". Both rescue something from being dismissed, but あながち is about truth or correctness, while まんざら is more about value and feelings. Only まんざら forms the set phrase まんざらでもない.
Examples
褒められて、彼はまんざらでもない様子だった。
He looked rather pleased at the praise.
彼の料理の腕もまんざらではない。
His cooking isn't half bad.
田舎暮らしもまんざら悪くない。
Country life isn't so bad after all.
その話もまんざら嘘ではなさそうだ。
That story doesn't seem to be entirely untrue.
デートに誘われて、まんざらでもない顔をしていた。
When she was asked on a date, she looked rather pleased.