If you are judging Illinois athletics by having both football and men's basketball performing at a high level at the same time, the Golden Era may be 1949-1952. Though 1983–1989 and 2001-2005 may be up there.
🏆 1983–89 This era is unusual because both major revenue sports were legitimately good simultaneously.
Football
1983: 10–2, 9–0 Big Ten, outright conference champion, Rose Bowl.
1984: 7–4–1 and bowl-bound.
1988: 6–5–1.
1989: 10–2, Top-10 finish, Citrus Bowl champion.
Basketball
1983–84: 26–5, Big Ten co-champion, Elite Eight.
1984–85: 26–9, Sweet 16.
1987–88: 23–10.
1988–89: 31–5, No. 1 seed, Big Ten contender and Final Four.
And that 1988–89 combination is particularly compelling as Illinois football went 10–2 and finished in the Top 10, while basketball went 31–5 and reached the Final Four.
🟠 What about 2001–05?
This may arguably be the more impressive peak.
Football:
2001: 10–2, Big Ten champion, Sugar Bowl.
But football declined afterward: 5–7 in 2002, 1–11 in 2003, 3–8 in 2004, 2–9 in 2005.
Basketball, meanwhile, was outstanding:
2001: Elite Eight
2002: Sweet 16
2004: Sweet 16
2005: 37–2, Big Ten champion, national runner-up.
So 2004–05 is unquestionably the greatest basketball peak, but it doesn't qualify as the greatest football + basketball era because football was struggling.
If you want to define “Golden Era” specifically as “football AND basketball were good at the same time,” I will note that 1949–52 was historically impressive for basketball, with three Final Four appearances. Illinois finished third each time. And the greatest single season of Illinois football, perhaps, was 1951. The 1951 Illini went 9–0–1, won the Big Ten, beat Stanford 40–7 in the Rose Bowl, finished No. 4 in the AP poll, and are recognized by Illinois as the program's last national championship team. 1946–1953 was the greatest football championship era: Multiple Big Ten titles, Rose Bowls, and the 1951 national championship.
The data shows the current era has a ways to go before it is Golden.