We'd just stroll around the square entering every paved street. The old town is really nice, clean and small. Totally nothing like western Europe towns which are crowded with coffee and souvenir shops one upon another one.
I wouldn't come here specifically for the pagoda but as we were in the area and on the beach, we just went for a walk here. It's a small building but locals come here to respect it. I liked that it's kinda in the middle of nowhere.
It's a really nice place as there are many things to do, from eating to watching movies to playing games. You can easily spend there most of the day and never feel the time passed by.
Most of the tourist offices offer a tour to Karen villages to see the ringed women. It's interesting to see them but remember they are people, not caged monkeys to snap a picture from each side. They're kinda used to tourists and some want you to pay for the pic.
Venue has an interesting architecture which is hard to find anywhere else. If you're in town while any of the performances are on, don't hesitate and go for it!