Hi there,
It would depend on what area around Fuji you plan to visit.
A great place is indeed Fuji-five-lakes that you can access via Otsuki and the fujikyu railway from there.
An other great plan is to take the Shinkansen to Odawara and access the Hakone Area from there.
Hakone is home to some of the most beautiful views of Fuji.
Shizuoka and Gotemba are great places to visit with the JR Pass in case you don't want pay extra for local transport.
Last week I visited both and can certainly recommend them.
Gotemba has 10 great spots to enjoy the view of Fuji, it is also home to a premium outlet complex, so you can enjoy some shopping while viewing Fuji.
Shizuoka is a little futher away bus offers some great views of Fuji too! My personal favorite spot is from the top of the city all, there are also restaurants that serve Shizuoka green tea (some of the best in Japan) and offer beautiful views on Fuji.
Enjoy your trip!
-Daniel