It is probably impossible to say which language resembles Valyrian most, lacking a metric for similarity. But there are clearly identifyable influences of other languages, both constructed and natural.
Let's start with the catch phrase valar morghulis from GRRM: It just sounds like Tolkien's Elvish languages, with valar being a word from Quenya and morghul a word from Sindarin. Both Quenya and Sindarin have well-known influences from natural languages: Finnish for Quenya and Welsh for Sindarin.
Looking at High Valyrian, some Finnish feeling is still retained in the language: There is a distinction between long and short consonants as well as vowels, the case endings still have some Finnish feel (and a Latin feel, too, especially the vowel alternations), the phonotactics resemble Finnish. It is further away from Finnish than Quenya in its phonology contrasting voiced and voiceless stops and featuring the sound /q/. There is little Welsh in High Valyrian left, maybe the frequency of "the defining fantasy vowel" ae (Laura Wattenberg) can be traced to Welsh.
The 8-case system may be insprired by Languages like Russian or Sanskrit, with the commitative case being typologically rare, but occurring in Finnish again.
The four noun classes are a creative invention (but not far of, as natural language, especially Native American languages, are concerned) and I see no closer resemblence to Bantu languages (they have a lot of noun classes, but the noun classes are marked by overt prefixes that are also used as agreement markers).
The syntax with head-final relative clauses may be inspired by languages like Japanese.
P.S. While Peterson has stated some linguistic influences for the Dothraki language, I have not found a similar quote for Valyrian. So all the observations above are mine.