There are a number of options:
- You can use Blocktrades to instantly sell STEEM for ETH if you are not too worried about getting the best exchange rate.
- You can send your STEEM to an exchange such as Binance (link includes my referral code) where you can trade it at a better rate.
Then, as you say, you can send it to the public wallet address on your Metamask.
Feel free to join us on Discord if you need more help.