It’s been a very long time since I have visited the 5th station on Mt Fuji but I do not recall the roads to be overly bad as I too tend to get car sick on some roads. Also do not recall it being particularly scenic. I think it’s about a 2 hour drive from Tokyo. Tends to get cloudy later in the day. Not a problem if you are climbing the mountain as the trail is well marked.
Kyoto would be a very long day, hotel to Ueno station then train to Tokyo station, train to Kyoto. Probably 3 hours and close to $200 RT. Nikko would take a little less time but a lot less expensive.

Thank you, Kazu, for suggesting Kamakura. An excursion that includes a peek of the ocean would be very nice! Plus, we like that it is a shorter trip from Tokyo, so we could spend more time seeing things.
mrwunrfl, you live up to your name! Bookmarked Tokyo Cheapo - Okutama is beyond beautiful. Maybe a future trip for us.

We checked the Grand Sumo Tournament schedule - it's 9/14 - 9/28 in Tokyo. We'll have just missed it. Next trip, hopefully..
Cheers!