Why is in my tx another address, which receives 0.08BTC ?
That is the change address, the remainder of your coins are sent after deducting amount to your intended recipient and fees.
Where can I see this address in my Bitcoin core wallet ?
It isn't displayed in the UI. You need to go Help>Debug Window> Console and key in 'listaddressgroupings'. You should be able to see all your addresses.
I assume it is my change, but why is my change not 0.25 - 0.02 ?
Your wallet doesn't use the entire UXTO in the address for every transaction. It analyses and select the input which is most suitable for it. In this case, your wallet chose the input
https://blockchain.info/tx-index/233438884/1 to spend from. If you press 'show script and coinbase', you should be able to see it.
Your change is the total amount of inputs* - given as fee - the total amount of the outputs.
* Huge mistake on my part. Thanks HCP for correcting me. (More proof reading in the future i guess
)