If I understand your question correctly, you're planning to spend 3 weeks in Italy, spending about a week each in Florence, Venice and Rome. You want to know whether it's worthwhile visiting Siena as a day trip from Florence and whether it's worth a longer stay, right?
I've visited Siena both as a day trip and as a few nights stay, and I enjoyed both visits. If there are several things you want to do in Florence or other day trips you plan to take, then taking a day trip to Siena would be an enjoyable way to spend a day. I found plenty to keep me interested for a few days and there are lots of good restaurants, so that's also a good option, but the extra stop would probably mean taking a night each from Florence, Venice and Rome. If you're concerned about whether you'll like Siena, then go for the day trip option instead of committing to a few days.