3 or 4 nights in Kyoto?

I'm planning a solo trip to Japan in April. Kyoto is definitely on my list but I'm not sure if I should spend 3 or 4 nights there?

I'm planning to go to the following places in Kyoto:

Fushimi Inari, Arashiyama, Philosopher's Path, Ryoanji
and Kamo River / Gion probably.

I'd like to visit Kobe and Nara as day trips, and probably Himeji Castle too. Is that feasible or too ambitious? Or should I stay in Osaka and make day trips from there?

Thank you!

Difficult to judge without knowing your preferred style and pace of travel.

Fushimi Inari, Arashiyama, Philosopher's Path, Ryoanji
and Kamo River / Gion probably.

To the average tourist I would recommend two full days to see the above sites.

I'd like to visit Kobe and Nara as day trips, and probably Himeji Castle too.

Himeji is an additional half day. Nara and Kobe depend a lot on how much you want to see. You can easily spend an entire day in Nara. Not sure what you want to see/do in Kobe. You may be able to combine it with Himeji into a full day.

Or should I stay in Osaka and make day trips from there?

Considering that you spend 2-3 days in Kyoto, but none in Osaka (or do you?), I recommend to make Kyoto your base. Nara is easily accessible from Kyoto. And Himeji and Kobe, too.