Hi Leka -
As I see it, I agree with Akshit; by using Present Perfect tense, you are stating that you have the EXPERIENCE.
Present Perfect: "Have you (ever) been to Europe? Yes, I have been to Europe."
This has a totally different feeling than,
Simple Present: "Did you go to Europe? Yes, I went to Europe (last fall.)"
The first one is not specific to the time, but just let's the other person know that you did it sometime in the past. The second can be more specific. Often, with Simple Present you can ask and reply by telling 'when' you did something.
To answer your question, I would be surprised if someone used the Present Perfect in a sentence with the word "Today." It sounds a bit unnatural. Go for the Simple Past, it's less awkward.