I mean, I'm not sure myself what would be good, but here's a link to r/speedrun. It's probably not an uncommon question.

https://www.reddit.com/r/speedrun/comments/6od171/free_game_to_speedrun/

Any game that has basically no end to it. If it's like open world mmorpg or something that only has quests, then the whole game probably can't be done in a speedrun. Maybe the quests, but you'd probably have to reset so much that it just gets unappealing really quickly. Tycoons and simulation, too, probably. The only way you could speedrun the "impossible" games like these would probably be setting end game goals, like how there are different categories in games to speedrun (like doing star% or nipple% in SMO, even though those are basically meme categories). Basically anything can be speedrun (ran?) if you can set a goal in it. Even if it has no official ending to it.

How's it goin'? I'm interested in speedrunning, and I need some ideas for games to try running. One of the few games I can think of speedrunning is Pewdiepie: Legend of the Brofist, but I also have games like Plague Inc. and Rebel Inc., all of these being on mobile for me. Of course, these are way less popular, so I also want some ideas on the more popular games. I've seen SMO, BOTW, and SM64, but I can't do those just yet. Any ideas for PC games, emulated or not? I can also do some mobile games. Keep in mind, still not very experienced in actually doing the speedruns myself, but I'll try any difficulty since I learn relatively quick.

The impossible 100% category though. Completing all levels, collecting all badges, all attacks and defenses, all characters, all modes completed (including Pug mode), and maybe all achievements. Depending.

(Also, apparently no one plays it on mobile??? I mean, it's just single player basically, but still.)