You get pretty good views of Fuji just from the train itself. Unless you're planning on getting a lot closer - car hire, bus trip - then it might just be 'good enough'… it's not small, you can see it from Tokyo on a clear day, 100km away;)
I've driven around it on the tiny roads in the area & tbh, you can't see it a lot of the time, if you get too close. It was very wooded where I was, though we were specifically aiming for an onsen in one of the small villages [I forget which.]
I think it's one of those instances where the closer you get, the less you see. The phrase, "You can't see the wood for the trees" springs to mind.
Planetware has a guide on getting to Kawaguchiko [& a good picture of Shinkansen & mountain for a sense of scale], which is over the opposite side [North] from the Shinkansen line. That's kind of the 'centre' of the five lakes district. I'm not sure how dedicated you'd need to be to want to do that just to see what is in effect a triangle shape from all directions - it's impressive because of its sheer size, but it's a pretty simple cone shape from all angles - except you get to see it over water rather than just over flat arable land. I'm not sure it presents a 'best face' from any particular angle, though if anything, the sun is going to be from east/south/west depending on time of day so the Kawaguchiko aspect is likely to be in shadow for some of the day.
This picture is from perhaps 25km away. The drive to Kawaguchiko from Fuji [town] is about 60km by the shortest main route, 90 by the prettiest. If you want to get any closer, you're into some really twiddly roads - not too bad for me, I'm a Brit and used to driving on the left - but you really can't see anything further than the trees at the side of the road for mile after mile until you start to get close to or above the tree-line… by which time you're far too close.
Near the treeline, it starts to open up bit…
This is as far as you can go by car up the Skyline Road… your best view from here is back down the hill.
Pics from google