Go to reliable exchanges such as Coinbase, Bitstamp or Kraken.
Cex.io usually have a much higher BTC price, so I wouldn´t recommend it.
Coinbase, Bitstamp and Kraken are all pretty thorough as far as identity checks are concerned. Last time I had to update some personal info on Bitstamp it took a few weeks to update, but that was during the height of the bull market so things may proceed faster now.
While I also wouldn't buy 30 BTC in bulk via LocalBitcoins it may be worth trying to buy smaller amounts via multiple sellers. Be aware that some of the more professional sellers nowadays ask for IDs as well, however that process shouldn't be as lengthy as your standard exchange KYC procedure.