You're absolutely right to dump Coinbase -- they're the direct defendant in a lawsuit by the IRS to get YOUR trading records.
But Kraken has a lousy reputation in the bitcoin community, too. Their charts are hard to read, they constantly break down and their live markets aren't very live. Instead, you might want to consider:
1.
https://www.bitstamp.net/ -- If you're not concerned about alt coins (they only trade BTC, XRP, LTC and ETH) and don't mind a lack of margin trading and short selling, then Bitstamp's a great option. They're fully EU regulated, incorporated in Luxembourg and operate out of Slovenia, so they're completely independent of whatever precedent gets set in the IRS vs Coinbase decision.
2.
https://www.bitfinex.com/ -- If you're not located in the US, Bitfinex allows completely anonymous trading. They offer about 15 alts, margin and short trading.
3.
https://bittrex.com/ -- If you like alt coins, Bittrex is THE place to be, offering over 100 coins. They're US based, so they will be subject to the precedent set in IRS vs Coinbase, but they allow some small stakes anonymous trading. If you verify your ID, they also offer margin and short selling.