If you’re wanting that Nancy Drew feel, I’d recommend reading the books the games are based on. There’s a post at the HER boards that lists which books were used for which games. It’s really interesting to see the similarities and differences.
If you liked Ghost of Thornton Hall, you’ll like the Thirteenth Tale, and the Distant Hours. Both deal with families, and secrets and both use fire as an element in the story.
If you like the cozy feeling of Nancy Drew games, then you’ll like cozy mysteries. My favourite series are: The teashop mysteries by Laura Childs, Jaine Austen by Laura Levine (very humorous), Lexy Baker mysteries by Leigh Ann Dobbs, The Cupcake Bakery mysteries by Jenn McKinlay.
I’d also suggest “Murder She Wrote”, both the book series and the TV show. Jessica Fletcher is like a grown up Nancy Drew basically.
Artifex Mundi games: These are great games. They’re slightly HOG, but it’s kept to a minimum. I’ll go into more detail on each series.
Grim Legends: The first two are based on fairy tales and have a dreamy quality to them. My favourites. The third is not based on a fairy tale, but is enjoyable all the same.
Enigmatis: These are very Nancy Drew like. You have to solve a mystery in the first one, and the second and third deal with the outcome of the first one. Very enjoyable!
Nightmares From the Deep: I’ve only began playing these, but they remind me a bit of Sea of Darkness as there’s a museum in the first one, and you go on a ship as well.
New York Mysteries: I’ve only played the first two, but they’re really good. They’re a bit Nancy Drew ish in that you play as a reporter who is trying to solve these strange mysteries.
(The above games contain supernatural elements. Avoid if you don’t like that kind of thing.)
Her Story: A wonderful game where you watch different videos of a woman being interviewed about her husband’s disappearance. Feels very Nancy Drew-ish as you try and work out what happened.
Gone Home: A beautiful story. You go home, and search through your house for information on your family, and what’s happened while you were overseas. Nothing scary, and just a lovely story.
Life is Strange: An amazing game, probably one of the best & most impactful games I’ve ever played in my life. Focuses on a teenage girl trying to solve a mystery at her school. Very coming of age and all.
The Wolf Among Us: LOVE THIS GAME. Set in New York, basically old fairy tale characters living in NY, and you play a detective who is solving a mystery. Beautiful art, great music.