Hi Anne,
For a trip such as this I recommend purchasing individual tickets as needed to get between locations and perhaps looking into the following municipal tickets if you think you'll be doing a lot of travel within each city (this would certainly be a good option for Kyoto I think):
It could be that you'll do enough to warrant a 2 or 3 day Kansai Thru Pass, however you'll need to factor in some projected costs for this based on how much sightseeing you think you'll do, and also will need to use non-JR transport between cities (not a huge issue).
Kobe is very much doable from Osaka at ¥390 each way. Here's a sample itinerary for you to base your travel off.
Hope this helps!