Here's a good site. https://www.visitnikko.jp/en/

Although Lake Chuzenji is lovely, it's quite big. Not exactly walkable. It's best to have a rental car to see some of the waterfalls that are up there.

Nikko is famous for Toshogu Shrine with the three see/hear/speak no evil monkeys. There are other nice temples and shrines within walking distance.

https://www.japan-guide.com/e/e3801.html

Lunch at the historical Kanaya Hotel is a treat for me! (Not traditional Japanese. )

https://www.kanayahotel.co.jp/en/

Not sure what you mean by "downtown," ie by the train stations?

With just day tour, it would be difficult to do both the lake and Toshogu if you don't have your own car.

Hi, close to the temples I had a nice lunch at this family restaurant:

https://www.tripadvisor.com/Restaurant_Review-g298182-d3937069-Reviews-Sanraku-Nikko_Tochigi_Prefecture_Kanto.html

Why not just get the bus to the lake and back?

And while doing the shrines and lake in a day (I prefer doing the lake/Kegon Falls in the afternoon) you can do both in a day without too much trouble.

Thank you everyone! Once at the lake, Where does the bus drop you off & pick you up? How often does it run?

You will get off at Chuzenji Onsen, then walk to Kegon Falls and the lake. Scroll down to see the bus stop.

https://www.tobu-bus.com/en/nikko/

About Chuzenji Onsen. Scroll down to see the map. https://www.visit-tochigi.com/plan-your-trip/things-to-do/1077/

Here's a good website. https://www.visitnikko.jp/en/plan-your-trip/getting-to-and-around-nikko/