Here is a wikipedia page that pulls together almost everything you want, and for much more than just American English:
IPA chart for English dialects
It lists all the lexical sets for English vowels for many major dialects of English, showing where individual dialects merge or distinguish within some of these sets.
But IPA, much more consistent than English spelling or the pronunciation guides given by dictionaries, just doesn't do what actual hearing does. For that, use
to check individual words, what they really sound like in reality. IT is not organized by lexical set or dialect, just by the official spelling of the word and whatever person randomly decided to pronounce the word (with a geographical tag for that person to give you an idea of accent).