何（なん）といっても is an expression that is used in almost exactly the same way in Japanese as it is in English, and qualifies that ‘no matter what is said, (A)’, or ‘by any account, (A)’. Being a mix of the substitute noun 何（なん） ‘what’, or ‘whatever’, と, the て-form of the う-Verb 言（い）う ‘to say’, and も, the literal meaning is also ‘even whatever one can say (A)’.
何（なん）といっても is used primarily at the beginning of sentences, and frequently highlights something that is a positive aspect of (A).

• あのカフェは何（なん）といってもコーヒーとアイスクリームが安（やす）いからとても人気（にんき）がある。
  Without a doubt, they have cheap coffee and ice cream at that cafe, so it is very popular.
• 彼（かれ）は正直者（しょうじきもの）だし、話（はな）しやすい。しかし、何（なん）といっても誰（だれ）に対（たい）しても優（やさ）しいからみんなに好（す）かれている。
  He is honest and easy to talk to. But, by any account, he is nice to anyone, so he is well liked by everyone.
• 私（わたし）の日本語（にほんご）の先生（せんせい）は厳（きび）しいけど、何（なん）といっても日本語（にほんご）を教（おし）えるのがものすごく上手（じょうず）だ。
  My Japanese teacher is strict, but she is very good at teaching Japanese without a doubt.

Like many uses of 何（なに）, the pronunciation change to 何（なん） is simply for ease of speech.
Despite being used mainly in positive situations, 何（なん）といっても may occasionally appear with a negative nuance as well, although this is far less common.

• 彼（かれ）の悪（わる）いところは、何（なん）といってもすぐに嘘（うそ）をつくことだ。
  The bad thing about him is, by any account, that he is quick to lie.