Go read Eyes Turned Skyward.
Really Eyes wasn't terribly plausible. It's a nice fantasy story, and was miles ahead of any space AH I am aware of written before it came along, but space history has come a long way even in the short years since Eyes was written and space AH has come even further. So things that seemed plausible when Eyes was written are now known to be economically or politically impractical or just bad engineering.
In all honesty, the Saturn V's days were numbered before Apollo 11 lifted off and the Saturn IB had its goose cooked by the Apollo 1 fire.
There is an extremely slim possibility that instead of the Shuttle the US might have re-started the Saturn IB production line, but the rocket, for all the advantages we can see in hindsight, did not look good if all you have to go on is what was known in 1970 when solid rockets or reusable LOX-hydrogen rockets looked to be the wave of the future and Titan was the best of current technology.
And since the Saturn IB and Saturn V are difficult for NASA to keep flying, Apollo is difficult to keep flying as well.
The most likely alternative to the Shuttle is a civilian space program built around Titan rockets, likely either with a "big Gemini" capsule or (more likely) with a glider like the HL-10 or (with larger relatives of the Titan) a mini-shuttle with maybe 5 tonnes cargo capacity. All hopes for manned programs reaching beyond Earth orbit would be ruthlessly crushed by Congress, but a more interesting space station program to succeed Skylab (something like the Soviet Salyut stations) and the development of practical NERVA rockets are possible.
If NERVA results in actual flying nuclear rockets, then things could get rather interesting. But the engineers would need to win over the public and Congress on safety and Congress would need to be reassured that NERVA derived technology wouldn't suck the US into an expensive Martian quagmire (well, quagmire from their perspective).
fasquardon