We attended the wedding of a friend in Prague 1.5 years ago and it was a lovely place.
For a special evening, you could have dinner on the terrace at the U Prince Hotel in the old town. We had drinks on the terrace at sunset and it was very nice.
For something less formal, pack a picnic and head down to the old castle, Vyšehrad. It's quiet and peaceful.
BTW: For the best experience at Prague Castle, arrive at least an hour before St Vitus cathedral opens (9am). I did this one day and there wasn't a single other tourist in the castle, just employees. Minutes before the cathedral opened, the tourists came pouring in.
We did day trips to Kutna Hora and Cesky Sternberg, which were both nice.
We enjoyed a simple Czech restaurant next to the IP Pavlova subway station. Thanks to Google street view, it looks like the name is U Graffu. When you enter, it just looks like a small bar, but go to the left of the bar and down the stairs on the right to the restaurant. Good Czech food at good prices and good service. There wasn't much English spoken there, but we managed just fine.