As a non-native speaker, I find this one of the most frustrating features of English. Sometimes it rhymes with “call”, sometimes with “shall”. Some words, like “mall”, appear to have both pronunciations, and usage differs between British and American English. Any rules that I can rely on to determine, for instance, how to pronounce the name of the not-so-important English village of Albourne, Sussex, when I first come across it?
Good one, Pall Mall is like that.
I think you’ve identified one of the key rules already: always start by answering the question: “Am I trying to pronounce UK English or American?”
All else differs (or at least usually does) depending on that.
Sorry. 
It also depends on what part of America it’s being spoken in, if you’re talking American English.
In American English I think you’re pretty safe if you rhyme all “all” words with “call.” Or all, for that matter. “Shall” is probably an atavism left over from the Brits.
In addition, I have never heard “mall” pronounced to rhyme with “shall,” so that would seem strange to most local speakers.
Cities present far more problems. Some that start with “Al,” like Albany, the capital of New York, use the “call” pronunciation.
Probably more, though, rhyme with the name “Al.” Albuquerque, Alexandria, Allentown, Altoona.
What the Brits do is known only to the BBC.
As you are no doubt already aware, there is no reliable way to predict the pronunciation of English placenames from the spelling, even when we exclude from consideration oddities like Frome or Worcester. 10 years ago in a work context I often had reason to refer to the town of Lynemouth - I still don’t know the correct pronunciation. Each of the first and second syllables has two possibilities, for a total of 4. Similarly with Albourne, I wouldn’t hazard a guess as to whether the second syllable is /bɔːn/ or /bən/. So no.