Everyone knows about doing alchemy while doing agility, but that's far from the only activity you can do while churning though thousands of alchs, and I've found it's best to do it while doing activities that force you to sit still and wait for something to happen, or something to respawn.
I will admit that most of these suggestions are geared towards ironmen, but I think at least one is useful for regular accounts too, most notably:
Farm orange (or other) spices at the Hell-Rat Behemoths.
Reduces alchs per hour by about 150-200, and can be slightly more if you have to watch your cat regularly (Wily Cats have a damn near 99% win rate against the Hell-Rat Behemoths without any food for support, but you should still bring some. Other cats have much worse success rates and will require food basically every kill).
Telegrab wines of Zamorak.
Obviously, you will want to do this one at the Falador chaos temple, not any of the wilderness ones. Works best if you have access to the items necessary to get air, water, and fire runes provided by your equipment (such as smoke battlestaff + tome of water, or mist battlestaff + tome of fire) because you'll want alchemy runes and Teleport to Falador runes. A rune pouch can save an inventory spot by consolidating law and nature runes, or an elemental rune that you may not have the equipment to cover (preferably water, because you will consume by far the least of those, or air + water, if you have a divine rune pouch but only a staff of fire). Otherwise, follow the typical strategy for this on the wiki: https://oldschool.runescape.wiki/w/Money_making_guide/Collecting_wine_of_zamorak Note that telegrabbing has a huge animation delay, as well as your trip to bank the wines, may reduce your alchs per hour by as much as 300-400.
(meme suggestion: this, but telegrabbing the teak plank spawn in Prifddinas instead. Bring a plank sack
)
Collect Seaweed Spores.
This has the benefit of barely draining any alchs per hour at all, probably no more than 50, excluding the time you'd spend actually harvesting seaweed if you need/want it. You can't swim when you do this because you'll have a fire staff or tome of fire in your hands, unless you keep the fire runes in your inventory, so be careful around the deep water! Good way to get them instead of fighting lobstrosities, which is faster but far more annoying and is a dedicated effort.
Your ideas?
Most minigames, including ones that are OSRS content, don't allow alching inside of them, even during explicit waiting periods, so that's out. The ones that do allow alching usually keep you too busy, without any extended idle times. But I want to know your ideas too.