Linlithgow is a small village about half an hour drive from Livingston (outskirts of Edinburgh) and it is a pretty place to go and see swans in the large lake around Linlithgow Castle.
There are so many swans in this lake, that we nicknamed it "Swan Lake". They're always happy to receive bread, so bring a loaf with you.
You can explore the castle during the day, and often at night there are historic plays/concerts that you can go to, which are held in the castle. We've not been at all, but you can find out more information from Historic Scotland.
There are some pleasant walks around the castle and its surrounding grounds. In summer, the paths are lined with these pretty pink flowers, thistle and very tall green grass. We followed the path one day, which led us to a freely accessible farm that we walked through (dodging cows, sheep and horses). We strolled, and it took us about two hours.
Thistle is everywhere in Scotland, so it's no wonder it's called the Flower of Scotland. It looks very much like a weed, in the wild, but close up it is pretty and forms a nice contrast against green grass. (It also makes for good closeup practice!)