For the original question (BOAC days), the first 747 route is well known, LHR-JFK, but the second is less so, JFK to Bermuda. The same aircraft could manage the whole lot within a 24-hour rotation, day after day.
After several other North American points the aircraft then got put onto Jo'burg via Nairobi, and then some Far East/Australia, both the latter via various combinations of Frankfurt and Rome, not for range reasons but just for traffic. This pretty much covered the 747 ops in BOAC times.
The California service has long been something of a fascination; as far as I am aware BOAC never ran the 747 there, and shortly after the BA merger the Air New Zealand DC-10 arrangement started. Both Pan Am and TWA did run nonstop to LAX/SFO with the -100, but it was regarded by BOAC as extreme on range, and they used operating techniques BOAC did not wish to follow. Certainly comments from ATC at the time about the summer midday departures westbound from Heathrow, especially if on easterlies off 10R (now 9R), showed a certain genuine concern given the known reliability issues with the JT9D. Once gone, a bit of humour returned, Pan Am sometimes being described as having been a "Hedge Clipper" or TWA as "Departing via the Piccadilly Line".
BOAC traditionally ran on from California, generally San Francisco via New York, through Honolulu to both Stydney and to Hong Kong via Tokyo, and both these generally carried more US than UK-originating pax, but these were progressively given up. British AW was a bit thin on capital expenditure at first, but the first 747-200B/Rolls Royce delivered late 1970s were immediately put onto LAX as their first run in lieu of most, but not all, of the Kiwi DC-10s, and then started a San Francisco flight as well, finally having their own aircraft with the range.
I was a bit surprised in about 1996 to get a BA 747-100 (in fact the pioneer AWNA), from Vancouver to LHR, which was my only -100 from the West Coast, but that's a bit shorter than California.