Actually Tobu World Square is off another station on Tobu line, so I would recommend an overnight stay if you want to visit there as well. Please have a look at the simple "Oritentation" map here (the bottom one):
http://www.japan-guide.com/e/e3805.html
From the station on the right, you have Toshogu Shrine, then to the left there is the "Irohazaka" winding (zigzag-looking) road up to the Kegon waterfall and the lake. Akechidaira ropeway is located on the way up the winding road. Yashio-no-yu is located between the winding road and the central NIkko temple/shrine area, just off where the darker gray road branches off the road marked in pale gray.
I would suggest going in the following order - take the bus up toward the lake, but get off at Akechidaira on the way up because you cannot access the ropeway on the way down. At the top is the lake and the entrance to the waterfall. You can come down after visiting the waterfall and the lake (there is a pleasure boat ride), then visit the shrines. There are many shrines that you can visit; we could easily spend half day only around the temples/shrines.
1) Akechidaira Ropeway
2) Kegon Waterfall
3) Lake Chuzenji
4) Tosho-gu Shrine
THEN, after this if you have the time, you could go to:
5) Yashio-no-yu
You would have to back-track a bit, though. This Yashio-no-yu is located 12-minute walk from Kiyotaki bus station (according to the city website). And this bus stop is located between the winding road and the central Nikko area.
The reason why I suggest going up to the lake first is (though it depends on the day) the traffic up/down the winding road can be quite busy. So I personally prefer to cover that segment first, then spend time in central Nikko later, where I am closer to the train station for the way back.