Hi
Localbitcoins are good if you need to buy/sell quickly as you can transact directly peer to peer without having to wait for long bank SEPA transfer times. That said you will pay a bit more on localbitcoins than you would on a proper exchange.
You can transfer coins from any wallet to any other and you will have a wallet automatically setup for you on your exchange/localbitcoin accounts.
I use multi bit as a desktop wallet and transfer from it and to it using localbitcoins or any other exchange that I have a wallet with.
You should never leave coins on a website online wallet, be it localbitcoins or any other, you should transfer them directly to your desktop wallet ASAP IMO !!
Hope that helps.
Is there any charges for transfering from an online wallet to a desktop wallet and vice versa?