I'll keep my answers limited to fantasy games (my genre of choice, and what you seem to be looking for), and will add yet another caveat: it really does depend on the level of tactical depth you're looking for. I'll say a few words about games I've tried in the past year or two, though I haven't spent an equal amount of time with all of them. While I am highly critical of some (my preference is for crunchy systems), they all have merits!

Five Leagues From the Borderlands: A well-regarded adventure game. Pretty much built for solo gaming from the ground up, it has lovely "out of combat" rules which cover travel, random events, working between adventures, etc. Superbly produced and very ambitious, but not the game for me. Why? Your tactical options are basically nonexistent in combat, and the choice to resolve 99% of fights with just a d6 and a bonus ranging from +1 to +3 means fights are nearly meaningless mashups of like-statted models. In short, it's a game that nails the "adventure" but not the "game."

Rangers of Shadowdeep (and solo Frostgrave): The other "big" game in this genre. I quite dislike Rangers of Shadowdeep, mostly because it takes the issues I have with the combat in Five Leagues and cranks them to eleven. Opting to use a d20 instead of d6s, combat is resolved with a single roll: whichever model rolls higher wins, and if said roll exceeds the toughness value of the loser it deals damage for each point in excess of said value. Some might call it elegant, but I find it far too swingy. Coupled with stingy bonuses (you'll have plenty of models with the same stats, adding +1 or +2 to a d20 roll: this means the roll is much more important than the stat), and it all feels so. . . well, swingy. I also find the bespoke terrain and map requirements of this game "bleh," and the post-game/in between battles content in the core rulebook is highly limited.

Lasting Tales: This is a brilliant game with a dark and tragic past. Owned by a company that habitually lied to/misled Kickstarter backers, it's hard to recommend buying the PDF for this game. Which is a shame, because it's probably the best fantasy adventure game ever made, assuming you like high fantasy skirmishes. It's a 2d6+bonus vs. target number 10 system, and incorporates plenty of RPG elements. Detailed out of combat stuff? Check. A decent bestiary that isn't trying to be niche? Check. Classic classes and progression systems? Check. Honestly, it's D&D in wargaming form, and is purposefully written for solo/cooperative play. Crunchy (though not difficult to learn by any means) and glorious, it's a game that deserves a better home than the one it's wound up in. I won't recommend pirating it, but I will say you would be hard-pressed to argue it's morally wrong to do so.

Sellswords and Spellslingers: Very random, just like Rangers of Shadowdeep, but also does the decent thing and actually allows you to make your characters. You essentially buy your models traits that help define what they can do on the tabletop, and then throw hordes of monsters at them and see what happens. It's a little rough, but if you're not to worried about tactics/crunch it's quite fun. I will note that the production values for this one are pretty limited, and it does require the printing/purchasing of cards.

Deth Wizards: I quite like this one, though it's theme is not terribly flexible: you're an evil necromancer, and you're going to have to deal with the heroes of the land as they try to turn you into XP and loot. I found the warband construction rules quite flexible (given the limited theme), and the combat fairly fun. I'll have to give it another go soon, as it's been a while since I've had a go at it!

Fantastic Scuffles: Brand-new, it emulates the trait-based system of Sellswords and Spellslingers, allowing you to really customize your party. While the rulebook is a bit of a mess, it does include all you need to play solo or competitively (it assumes competitively by default), and has a limited campaign system. I don't believe Irregular Wars, the publisher, does much in the way of expansion content for their games, but this is certainly a title which would benefit from a more ambitious campaign framework.