I'm only finding Iridium in breakable, random items. Where can I find it otherwise? I assume there's some level of the mines, but which ones?
Iridium can be found and mined in the Skull Cavern in the desert. Once you have reached the bottom of the mines and fixed the bus, go to the cave in the top-left of the desert. The enemies there are tough but you're much more likely to find iridium and there's more of it the deeper you go.
Additionally, (spoiler if it is not year 3)
If you earn the best score (all four candles lit) when your grandpa evaluates you, he'll give you the Statue of Perfection which produces iridium ore.
They are very rare. I have found them in levels past 90. You can also get one from the traveling wagon sales lady. She will occasionally sell Iridium ore, bars and sprinklers.
I just got the bus fixed and it takes you to the Deseret. You can go in the cave and get Iridium drops off the mobs in there.
Skull Cavern is great for Iridium but only if you can get past level 100 before you fall asleep. Before level 50 Iridium is scarce. The best way to descend quickly is to spend about 250,000 gp on Stone, then keep on building Staircases. imo buy about 40 bombs from the Dwarf too.
I did this and ended up with 250 Iridium Ore in one day + 3 Prismatic Shards.
To raise the 250k, imo the best way is to grow a lot of the most lucrative crops which imo are spring = Cauliflower (or even better is Strawberries). Summer = Blueberries. Autumn = Cranberries. Consider using Kegs to boost their value.
Minor spoilers ahead about stuff ~year 2
Unlike copper, iron, and gold ore veins, Iridium ore veins will not spawn or generate in the mines. You can receive them from Omni-Geodes, which you can theoretically find at all levels of the mines, but will really only appear frequently towards the last levels of the mines.
After you reach the "end" of the regular caverns, you receive the skull key which grants you access to the skull caverns. To access the skull caverns, you must first repair the bus by completing the vault bundles (bundles unlocked after completing five separate bundles), which only ask for gold not items (42500 gold total to complete all bundles and repair bus). After you have done both of these things, you can pay the 500 gold bus fare and ride to the Calico Desert and access the Skull Caverns, where Iridium ore veins will spawn. Because the nature of exploring the caverns is very different from exploring the mines (I wont explain unless you want me to, it's a big gameplay thing), the goal in the caverns is to descend quickly, because for every 10 levels you descend, the probability for finding iridium increases (As noted in here, 4th bullet point) So, just try to get down as low in the Skull Caverns as you can. I recommend you bring food.