You might enjoy two of my games.
Fable on your Table is a kind of tabletop miniatures RPG with a companion web app that lets you delve into a dungeon solitaire. Includes what I think is a pretty cool "2x2" resolution mechanic that offers a lot of fun detail and mechanical depth. To get the full experience, you need to cut out and assemble the minis and terrain, but technically you could play it with graph paper and pencil.
Dungeon Hero is a pared-down version of the above game's mechanics, boiled down to fit into a "zine". A "zine" is one piece of paper folded into a little eight-page booklet. Dungeon Hero uses a similar resolution mechanic as Fable on your Table, and comes with some little booklet adventures that you can play solo. This system is much simpler than the other one, out of necessity given the small footprint, but it manages to pack a lot of action into the little "zine" adventures. Also, the adventures are all inspired by classic old-school tabletop adventures, so they are designed to recapture some of those vibes you're asking about.
Both games have some videos you can check out of the gameplay if you're interested.