Advice - Osaka or Kyoto as a base

My partner and I will be travelling to Japan for two weeks in February with our (then) 10 month old daughter.

I was just wondering if anyone could offer their advice as to which city would be better to use as a base - Kyoto or Osaka.

Would we be missing out on anything if we didn't stay overnight in one of those cities?

We had originally planned to stay overnight in both cities but we were thinking it may be easier (with the baby) just to use one as a base so we don't have to worry about moving our luggage around too much.

Also, is it possible to explore Himeji in about 3 hours (on the way to Hiroshima) or should we allow more time?

Any advice would be gratefully received.

It depends on where you want to go but as you plan to go to Hiroshima (and may some other places?) I think Kyoto is better than Osaka.

In Osaka, station for local trains and one for Shinkansen (bullet trains) are different. (Bullet trains do not stop at Osaka but Shin-Osaka station) Kyoto stations are both for local trains and for shinkansen.

Both cities are worth seeing for different reasons. Some tourist prefer Osaka for the night life but with a baby I don't think that it is one of your priority?! I like Osaka because of the huge underground shopping malls, amongst other things... but I actually prefer to stay in kOBE !. in your case I would recommend Kyoto. Yes you can see Himeji castle in 3 hours if you don't dilly dally between the station and the castle and don't try to explore every nooks and cranies of the gardens around the castle. It is definitely worth seeing, especialy if you are familiar with medieval European castles.

------Also, is it possible to explore Himeji in about 3 hours (on the way to Hiroshima) or should we allow more time?-----

I would allow more time and do each on different days. I think it takes about 45 minutes from Osaka to Himeji so you need to give yourself time to tour especially with your 10 months old baby in tow.
Osaka seems like a good place to base yourselves if you are planning to see Himeji which is near Osaka.

Thanks so much for the advice. It has been really helpful.