How to find what is suitable transaction fee to send 10 mBTC? Using MultiBit Desktop Wallet, I can see that the default transaction fee is set to 0.5 mBTC per KB. 

Usually that default rate worked fine. But yesterday, when I tried that and my transaction has not been confirmed for over 12 hours now. 

So today I increased the fee to 1mBTC per KB and tried to send another 10mBTC to the same destination wallet. It is half an hour now and it has not confirmed either.

It is really frustrating. I'm wondering what is wrong here, and how can I choose a fee that make near instant transaction possible.
Bitcoin Fees is a useful site to see the current network status and pending transaction fees. According to that site as of now, a transaction fee of 4.11 - 4.20 mBTC/KB is required to clear within 1-12 blocks (i.e. within around 2 hours), 4.61+ to clear as soon as possible.