I was born in Burien, Washington. Although we moved when I was two, it was to a town only about 10 minutes away. I was therefore very familiar with it throughout much of my growing up years. Burien is one of the lucky towns of Washington to be on the waterfront of the Puget Sound. That is not the only obvious natural attraction. Like much of Washington, Burien has a great view of the mountains. Front and foremost is Mt. Rainier, the enduring pride of the Northwest. (How I love that mountain.)
If you visit Burien, Washington, you may need to know where to find a good airport. Sea-Tac Airport is the main airport of King County and is only five minutes from Burien. While here you may also want to be aware of some significant towns in the area. The biggest, debatably most beautiful, and probably the most famous city in Washington is Seattle. It is only about 10-15 minutes away from Burien. If you are coming to visit Burien, you absolutely must visit Seattle. About half an hour south, you will also find the big city of Tacoma.
I have not returned to Burien in 22 years so I'm sure a lot has changed. I recently read that Burien has been proactively making a whole lot of changes especially in recent years. In my mind, although I never considered Burien amazing or even that interesting it will always retain the innocence of my youth. If I were confident that Burien were still as I remember, I would urge you to make it your headquarters (where you sleep) while you visit the much more interesting sites like the rest of the waterfront, the city of Seattle, Mt. Rainier, and even the ocean.