I went to Kegon falls (although my main objective was Ryuzu falls). It was magnificent, but it is not easy to go unprepared so here are a few things I learned which hopefully will be of help to you.

1. The closest stop to Kegon falls is Chuzenji. When you get off, go right (opposite direction of the lake). You will be at the falls in 7 or 8 minutes on foot.
2. Near the falls are many souvenir shops. Most of them have same prices but sometimes they have slight differences. But their prices are still better than Tokyo.
3. You can walk from Kegon falls to Ryuzu falls. The trail is gorgeous but it will take you some 3 hours (maybe more, depending on your pace) so keep that in mind and go early if that's your objective.
4. Alternatively you can take the bus. The ticket from Tobu station to Chuzenji is 1150y, which means the round trip is 2300y. The 2-day free pass for unlimited bus use between Tobu station and Chuzenji is 2300y so trust me, take the pass. You will need it. If you want to continue on the bus to Ryuzu falls you will pay an addition 490y (one way). To sum up: move freely with the pass up to Chuzenji. Beyond that point you pay the additional infare cash depending on how far the station is.
5. If you come from Utsunomiya by train (which was my case), you will have to get out of Nikko train station, turn right and walk for some 20 minutes to find Tobu station. You can buy the pass there.
6. Both A and C line buses go to Chuzenji so you can take the one that you find.
7. Nikko specialty is yuba (tofu skin) and it's delicious. I tried it in both ice cream and croquettes and they were amazing. There is also Yuba ramen but I didn't have time to try it. Check out several restaurants because there is a whole range of prices.
8. I put pictures of the bus schedule to give you an idea.
9. The station Shinkyo is also a nice scenic spot to hop off the bus to take pictures of the bridge. But I don't think it's worth it to pay to cross it. But it's up to you! I hope this will be helpful.