1 day at Mt Fuji (from Shinjuku) worth it?

Hi,
My gf and I are planning on climbing Mt Fuji on the 1st or 2nd of July. We only can spend one day on site and where wondering if it was possible/interesting to come only a day and climb Mt Fuji.
Of course we understand we won't be able to go to the top but is it worth it climbing in one day.
If yes, where would be the best trail to climb.
Thanks in advance for your help.

I've never climbied Fuji in the "climbing season" as crowds on a mountain don't interest me. From the Fujiyoshida 5th station I was able to climb to the summit and get back down in one day by taking the first bus from Shinjuku to the 5th Station.
http://www.japan-guide.com/bus/fuji_season.html
In the off season, that's the 7:40 AM bus that gets you to the 5th station on the north side (Yoshida Tozando trail). From here to the summit was 5 hours. It was 4 hours back down. There were only 2 other climbers on the mountain at that time, though, and we grouped together as far as the crater.

If you get the 6:40 AM bus you can get off at the 5th station at 9:05. You could go up as far as time allowed along the trail, assuming slow hikers on the trail will cut into your time. I found glissading through pea-sized gravel on the descent was more fun and faster than following the trail. I don't know if with all those people in the summer whether anyone will yell at you for going off trail, but it would save time.

You'll find that once above the 6th or so station, the views get uninspiring; it's kind of like being in an airplane with nothing close by as high. On a clear day, you can get views as far as the Alps to the West and NW, as well as down on the 5 lakes region to the north.

You could also look into hiking down from the 5th station along the Yoshida trail to the Sengen Shrine in Fujiyoshida (vs taking the bus back down). This would take about 5 hours but you could see what condition the old stations are in. Last time through some were falling down as almost no one except foresters go past them anymore. Most of this section is through planted cedar.

Thank you so much for your answer, it helps a lot.
I think we will arrive the day before, stay in a hotel or so close by and climb early in the morning so we can get the last bus that leaves 5th station for Shinjuku at 5pm. I just hope it won't be too much a rush to get back down.