There are many places for both; use an online guide such as runescape.wikia to get a full list. Two place where you can get iron include south-west of Varrock, and south-east of Varrock. Look at the world map and look for the mining icon; it looks like a pickaxe. One place where you can find coal is in the center of Gunnarsgrun, also known as the Barbarian Village. Once again, you can find this on the World Map.
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You do not mine steel ore. Steel ore does not even exist! You may have thought that because of a steel bar. Well, to get a steel bar, you have to use one iron ore and two coal ores.
You have to mine iron ore and coal make a furnace and melt the iron ore to make iron ingot. Update: THANK YOU SOOO MUCH!!!!!!
You can buy them at the Grand Exchange. Although, it is preffered that you mine iron ore and smelt the ore into bars to raise your mining and smithing level and earn you profit.
The best ore to mine in free to play would be iron ore. Iron ore should be mined until level 99 in free to play and until level 65 in pay to play. Iron ore mines much faster than coal and re-spawns extremely fast. At level 65 in pay to play mine granite until level 77, then at level 77 mine concentrated coal until level 80, then at level 80 mining mine concentrated gold until level 99.
You mine diamond ore with a iron pickaxe or better, that means you can only mine it with iron or diamond picks.