I will go with localbitcoins.com as I think that is most convenient wallet as I need to transfer my btc to my bank account and localbitcoin is the best as the transfers are done in fraction of minutes.
Its an exchange and that is how it is meant to be used, keeping your bitcoins in an exchange is a bad idea. If it gets hacked you can bid good bye to your coins.
I too use localbitcoins.com and Blockchain.info, both are highly secure. In terms of trading localbitcoins seems to be the best with lot traders with good price margin. Also in less time transactions were made.
They're secure but don't keep more than you can afford to lose.
Do local bitcoiners always have to trade with locals, or is that just a title for the wallet holder and nothing more?
Its meant to find the traders near you so you can do easier cash trades/bank transfers etc. but that is not it is only limited to, you can trade with anyone as long as you accept the terms of the trade and payment instruments.