You're going to love your trip! I went in January to both of those places and loved it. Okay, two things I learnt were that there are two types of free pass tickets available. You can get a two day bus pass that you can use to get on / off many busses. You can go to all of the attractions around Lake Kawaguchiko and Lake Saito, then you can use it to go to Fujinomiya and see the attractions around there. Price is 2,500 for adults and 1,250 yen for kids. Google: fujisan-west side story If you have an extra day I recomend checking out Hakone, you could get a combination ticket from Shinjuku station that will cover all your train travel, pirate ship rides on a huge lake, rope ways, and cable cars, and discounts for a lot of attractions. Amazing place! Google: odakyu passes hakone Hope this helps.

The food we found was on the way to the shrine, not near station, though there looked like there were some restaurants on the way back from the shrine to the station.

Train to Fujinomiya station, then a short walk. HyperDIA is a great timetable guide that can help you get there.

One last piece of advice. Our train stopped in Shizouka for about 15 minutes before train to Fujinomiya. The train continuing on to Kyoto also went through Shizouka. We researched the location of lockers and realized that since Shizouka was a much bigger station it had way more lockers. We checked our bags in Shizouka and easily picked them back up there. Don't count on lockers in Fujinomiya.