There was no lack of options that were floated around, so there's a rather infinite number of scenarios.
Low-key option: more and more Skylabs, Salyut-style. Block III Apollo riding a Saturn IB. IT can last well into the 80's, or perhaps the 90's, but what's the point ? At some point or another it might be cut by Congress as unuseful.
High-key options: keep Saturn V and lunar exploration running, eventually leading to a lunar base.
You need a strong (presidential) decision to be made between July 1968 (when Saturn V production was SUSPENDED) and January 1970 (when Saturn V production line was SCRAPPED definitively).
Back in November 1968 Nixon hired nothing less than a Nobel Prize (and laser inventor) Charles Townes as a transition team space advisor. Townes report was published Janaury 8, 1969 and expressedly recommended to keep Apollo running.
Townes team was against a space station and against the shuttle, and Townes felt Mars was a bridge too far.
Unfortunately NASA administrator Paine bypassed Townes and went directly to Nixon... and VP Spiro Agnew. Nixon went with Paine opinion and created the Space Task Group. Paine asked for everything but the kitchen sink - space station and shuttle and lunar base and mars and $10 billion a year for NASA over decades, 3 times what Nixon was really willing to spend.
Nixon politely red the STG report and on March 7 1970 said "for $3.5 billion a year, build the shuttle. Goodbye."
Now had Nixon followed Townes advice... January 1969 is still not too late to save Saturn V. That rocket production line was just on hold.
As for the Soviets - since they had lost leadership of the space race circa 1965, they were in a defensive position that amounted to "we will do what the american do, mimicking them".
So had Nixon picked up the Mars option, the soviet had a symmetrical option on the shelves, a nuclear-electric Mars ship they called Aelita.
More Apollo ? build the L3M, the improved N-1F rocket, and the DLB lunar base (all are detailed at Astronautix)
Or perhaps the american will build a big space station ? fine, the soviet had the MKBS project.
What the Soviets did not have (before 1976 and Buran !) was a shuttle project. The soviet military hated it, the soviet aeronautics and rocket branches hated each other since 1960, when Krushchev had shut down bomber design bureau by the dozens and sold them to the rocket scientists, just because the future belongued to the ICBM and not the bomber.
The shuttle was half an aircraft and half a rocket, but on the soviet Union both sides somewhat hated each others.
So it took 7 years to shake the Soviet inertia and start a shuttle program... there's no trace of a soviet shuttle before 1976... even if nixon had started the US shuttle as early as January 1972 !