I would rank them as follows:
1) Uppsala would be my first choice by far as I think it has the most variety of things to do. It is also very easy to get to from Stockholm by train.
2) Mariefred and Gripsholm Castle is also an interesting day trip. If you go, I would make sure that you go when they offer a guided tour of the castle and when the weather is decent.
3) Sigtuna is very small. It has a cute pedestrian street and a number of rune stones, but there isn’t a lot to do when compared to Uppsala.
4) I am not sure why you have Nynäshamn on your list. I’ve only been there to take the ferry and I am not sure what interest it would hold for a tourist.