Your travel between Osaka and Kyoto options by JR are:
Time required: 0:28 Price:] 3,080 YEN by shinkansen, 10 min transfer at Shin Osaka Station to local train
Time required: 0:27 Price: 1,870 YEN by Limited Express Thunderbird
Time required: 0:29 Price: 580 YEN by Special Rapid Service

Those rapid trains are frequent. Just show up at Kyoto Station and get on the next train and get off at Osaka Station a half hour later.

Hilton Osaka is 2-min walk from JR Osaka Station. The Conrad is a bit over a mile so an inexpensive taxi trip or easy walk.

There is a Hankyu Railway train between Osaka and Kyoto that might be more convenient than JR to some spots in Kyoto.