In the U.S., if all you want to do is buy some bitcoins, then I think that LocalBitcoins is the best for newbies and the next best choice is Coinbase.
If you want to sell bitcoins, then LocalBitcoins is probably the only choice in the U.S.
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Avoid Localbitcoins for the next 24 hours.
They are dealing with a potential security issue and have temporarily disabled all bitcoin withdrawals.
The extent of the issue is not yet clear. Hopefully it will not destroy them, but until the dust settles you don't want to be transferring any additional bitcoins to their service.