Medieval or Medieval 2. They are turn based grand strategy games where you control cities and units on a world map and when units battle enemy units this is done in a real-time tactical mode so you get the best of both worlds.
The games do have flaws, most notable in the enemy AI, but unless you read about them extensively you can easily lose 20+ hours the games before you start noticing and depending on how much you like the games 20+ more before you really start to care. So in my opinion they are totally worth getting. Get Medieval 2 if your PC can run it and Medieval 1 if it can't.
And if you can live with a fictional universe (but no magic or demons and whatnot) I think you would enjoy Mount and Blade. It's not a strategy game but an action role-playing game, I guess, but it's a little hard to describe how exactly it works. There is a free demo though so you can just take a look yourself. I recommend it.
I'm sure Stronghold 1 and its expansions would appeal to you a great deal as well. You basically manage castles and attack or defend them. Just stay away from Stronghold 2.
Knights of Honor may be worth a look too. It feels pretty authentic. Personally, I found it too complicated to be really enjoyable for me, but your mileage may vary. It's well done and unique and has an authentic atmosphere. Maybe tehre is a demo you can try.
