Where do I find higher tier ores?

Higher threat levels generally mean more abundant ores, and ores of higher rarity. However, especially rare ores like gold or diamond can still be hard to come by, generally occurring only at the deepest levels of the planet. Personally, I'm mining level 19 planets for gold and maybe producing 4 ores by the time I reach the planet's core. I found two gems (8 ores) worth of diamond in the 1-9 planets, and haven't seen any since.

That said, planet type may have something to do with it. I've noticed that moons contain a more ores than I'm used to, in addition to being a bit easier to dig through. Desert and arid planets are super easy sources of iron, copper and coal since you can just dig into the sand to dislodge everything.

Some advice: hoard your iron. You'll want it for Sector Beta.

The two primary factors in ore distribution are depth and threat level. Deeper is better, higher threat level is better. Biome may or may not be a factor, but desert, arid, and moon biomes have blocks that you can dig through quicker, which means you get to the ore that is there faster. Furthermore, moons warm up when you're deep enough.

Note that all planets have obsidian if you get too deep, and obsidian is much harder to dig through than any other block I've yet encountered. Ore value doesn't jump to match the digging difficulty, so in my view digging through obsidian isn't worth it.

Therefore: dig down until you see obsidian, then dig out to the sides.

Also, keep in mind your current target. In the alpha sector, your goal is silver armor. In the beta sector, you need gold, iron, and coal.

N.B. This answer was written during Starbound beta. It reflects a universe generated before the first character wipe of beta.