The Vorkosigan Saga by Lois McMaster Bujold is character-driven SF/Adventure. But a number of the novels and stories are also mysteries.
If you're not too sure about SF, start with the (free!) novella
The Mountains of Mourning; it's definitely a mystery, and is sufficiently self-contained to stand quite well on its own. It's a super story, that won both of SF's highest awards the year it was published (the Hugo and the Nebula). This one is certainly worth your time, whether you continue on to any of the others or not.
If
The Mountains of Mourning convinces you to give the rest of the series a try, you'll probably want to read them in chronological order. You can find that order from the timeline included at the end of
The Mountains of Mourning.
These books are solid gold -- I cannot possibly recommend them strongly enough! Over the years, I've pushed them on many friends and relatives. Even the ones who "don't like science fiction" liked them.
The mysteries in the series are (at least) the novels
Cetaganda,
Memory,
Komarr, and
Diplomatic Immunity.
Ethan of Athos (a sort of a side-jaunt from the main line of the series) is also sort-of a mystery.
Xenophon
P.S. The most cost-effective way to buy the eBooks is as Omnibus editions; each of which includes more than one novel from the series. Those editions are largely, but not entirely in chronological order.