Skytree is worth the trip across the river, the view is truly stunning and from one point on the highest-level observation deck you can actually see the curvature of the planet. Annoyingly, you do have to pay a separate fee to go to the higher deck it's a do-it-once-in-your-lifetime-and-then-never-again type thing. Yes it's expensive, but you're getting a totally cool experience in return. You're travelling across the world, why not see the shiniest, tallest new thing?
If you go on a clear weekday morning, they hand out reservation tickets for a specific time, usually only about 2 hours after you pick up the ticket. Then you show up and pay to go up when your time comes up. I have some photos from the observation decks if you're interested.