Have you played Dreamfall Chapters? It's the latest game in The Longest Journey series, and it's one of my personal favorites now. Also, if you don't mind "different" types of adventures, Life is Strange and Oxenfree show a lot of creativity, and I thought they were both excellent. Oxenfree has no puzzles, though, unless you count the radio mechanic and the optional search for letters. Dreamfall Chapters and Life is Strange have puzzles, though they're generally not very difficult. Dreamfall Chapters' stronger puzzles were a little harder than the puzzles in Life is Strange. All have very strong stories.
I'm also really enjoying the new King's Quest, though it has some action elements I could do without. Depending on your tolerance for those, if you're a King's Quest fan, you'll probably like it. Reactions can vary, though, so you may want to watch a YouTube video to get an idea as to whether or not you'll enjoy it.
If you're looking for a more classic experience, Technobabylon is one of the stronger recent ones. Also, if you haven't tried them, you may consider The Book of Unwritten Tales games. The Book of Unwritten Tales 2 was just completed early this year. They're great classic adventure type games, and they have elements of both Sierra and Lucas Arts.
If you don't mind very dark games, The Cat Lady and Downfall by Harvester Games are fantastic, particularly the former.
And hopefully, The Last Crown: Blackenrock will be out soon.
Midnight Horror was definitely fun but more of an appetizer.
EDIT: I just realized you said you didn't like not being able to save your game. Unfortunately, several recent adventures are like this. I don't like it either, but I would be missing out on so many great games if I didn't tolerate it. So to let you know Dreamfall Chapters, Life is Strange, Oxenfree and the new King's Quest all have autosaves. I find them generally frequent, though sometimes it's a pain having to get to one. Oxenfree saves the game every time you enter a new screen, so in a sense, you can create your own save just by going to another screen if you like.
But if creating your own saves is an important factor to you, I wanted to let you know this. The other games I have listed here do allow you to create your own saves, so no problems there.