Have you been on a long trip away from home before? Even when it's an exciting journey it takes a bit of getting used to. If you haven't been away for long periods before I would recommend maybe one week in each location, so three weeks roughly in total. Just because that is almost a month and it isn't too much of a commitment. I found the first long trip I took away from home quite daunting personally! I had a great time but it was a bit of a crash course.
If you're really interested in exploring in depth then a least two weeks in each would be ideal. That way you allow for some locations to be closed for a few days (as can happen sometimes) without needing to rearrange your schedule too much.
Are you thinking of travelling to some areas outside of the cities, or staying within them?