Eric Davis is actually a really good guess, which I hadn't thought of. The Reds outfielder looked like a sure hall-of-famer when he came up, but his career was marred by injuries. Despite putting up several great seasons, including a season in which he posted 27 HR and 80 SB, his only 30-30 season came in 1987, when he had 37 HR and 50 SB.
The guy you're looking for *also* had a 30-30 season in 1987, with 36 HR and 32 SB. His other 30-30 seasons came in 1989 (36/41), and 1991 (38/30). He was primarily a 3rd baseman, but shifted to OF for a couple of years, and also logged time at 1st, 2nd, and SS. He came up with Detroit in 1982, and spent his last 2 seasons in Colorado and Chicago, respectively, but is mainly known for his 9 seasons with another NL team, with whom he won the World Series in 1986, a year in which he played only 88 games, and hit only 10 HR's.
I know this information isn't really much help, but I'm trying to skirt around telling you what team he played for, as that would really narrow down the choices to 2 candidates.