LocalBitcoins.com? (Is this safe? How are the prices?)
You're dealing with other people, so it's on a case-to-case basis. It's generally safe though. Prices shouldn't stray too far from exchanges, but exchanges are often better value-wise in my experience. You just have to check both when making deals.
The most private way to buy that I know of is to trade with fully anonymous crypto. Get Monero, exchange it for your coins of choice, and your identity should be fairly obscure. You could probably also do this in reverse if you're selling.