Huge, huge fan of puzzle games along the lines of The Room series, and House of DaVinci (where you open little secret compartments and construct tools and put things together and open up areas, align lights to turn on machines, etc etc so on and so forth).
ANY games anyone can think of like that they can recommend is greatly appreciated! 
Not exactly the kind you described, but do check Seasons After Fall. Puzzle/Platformer hybrid.
I haven’t played it yet so take my suggestion with a grain of salt but i was recommended to buy the Talos Principle. It’s a bit pricey though so you might want to wait until it goes on sale.
Soul Reaver 1, it has a very pleasing story in my opinion and the puzzles are there.
Definitely check this out if you haven’t already, my personal favorite puzzle game. It’s got many, many levels and some are really hard. If you get the Gehenna DLC they can get very difficult indeed. It also has a, to me at least, amazing story with tons of things to read.
Many games tried to emulate it and failed. I own a couple of those but won’t recommend them because they’re not very good, I just went over the two hours to refund them and now I’m stuck with them. Meh.
Definitely Talos Principle that was already mentioned, Quantum Conundrum was pretty fun, too!
Thanks guy! I’ve already beaten Talos Principle, Myst and Riven. Gonna check out those others.
Check out aphoria on steam. It was released last month, it’s not a bank breaker and is touted as a myst inspired game. I’ve been enjoying it.
SOLD! Now THAT is what I’m talking about!! THank you !!!
My pleasure mate, enjoy.