For romance, try Queen In Hyun's Man - it's one of my favourite romance dramas of all time. No cliches usually found in romance dramas, lead male is not the usual annoying jerk, and the whole time travelling mechanism was done really nicely with none (or at least barely any) loopholes. I really love this drama.
For investigative, try Special Affairs Team: TEN - seasons 1 & 2. I see that you are currently watching Vampire Prosecutor (also one of my favourites), and TEN, which aired on the same cable channel, shares some similarities with the VP series, although TEN is a little bit darker and more twisted. If you are enjoying VP, I think you would like TEN too.
