From what I gather from the era the next goals were pretty clear, even to the general public: "go to Mars" (or in the Soviet case "go to Venus"), and then go to Alpha Centauri.

If the Soviets would have won the race to the moon this might even have happened. But instead the Soviets decided to focus on space stations, and the US declared themselves winner and did largely nothing (by rejecting NASA's Space Transportation System proposal, which was also about a space station and a way to get there cheaply).

The space shuttle was a bad system for a number of political reasons. Its per launch cost was comparable to developing new heavy lifts or developing new missions to the outer planets.

Effectively nasa was spending their RnD money on opex and not getting any political capital back for it. Tragically the program had been set up with the promise of a space truck, if nasa admitted they didn’t deliver a space truck Congress would have been unlikely to fund a new program. Had the budget been allocated entirely to either technological development or novel explorations America’s willingness to fund nasa could have been substantially different.