I just recalled a few more games
Neverwinter Nights 1 and 2. Both are Dungeons and Dragons games in the Forgotten Realms setting, like the Baldur's Gate games. I need to replay the 2nd game, but the 1st one is very open with your character creation and options. You investigate a mysterious plague that is threatening the city of Neverwinter and, of course, it is just the tip of the iceberg. Many branching choices makes your experience very different, and the mod community still releases full scenarios and other goodies, I'm currently playing a Diablo I + Hellfire conversion.
The Witcher 1 and 2. I know, I know. I'm not talking about the 3rd game that might be a bit too much for potatoes. But these two were made with the NWN engine, so you might be able to enjoy this trend with the older games.
And something a bit different?
The Forgotten City. It started as a Skyrim mod, but the developer made its own game. This is a more linear story experience, but it could be a nice experience. You find yourself by a river with a stranger, and you are stuck there, and someone has disappeared, so you offer to go investigate. Next thing you know, you are trapped in a city underground, where it seems they are all living in the Roman era, and a mysterious Golden Rule makes everyone afraid: everyone will pay for the sins of one. It is a time loop game, it can get very philosophical.