Best and cheapest transportation

I will visit Japan in August for a very short time.
I will have a 3 day free time which I would like to go with my fam to Kobe, Kyoto and Osaka.
On August 26, We will depart from Shinagawa, Tokyo to Kobe.
Then we will go to Osaka and stay there for the night.
On August 27, we will go and see Osaka n stay at the same hotel.
On August 28 we will go to Kyoto and stay there at night.
On August 29 we will go back to Narita airport, Tokyo and fly back to Jakarta.
My question is what transportation should we use so we could get the best and cheapest transportation.
Any information would be highly appreciated

Trains, for sure. Kobe, Kyoto and Osaka are all very close and so a local train would be cheapest.

The main issue is that you want to visit the Kansai area from Tokyo. Why don't you fly into Kansai Airport instead? Tokyo is 2.5+ hours away from Kobe/Kyoto/Osaka.

What are you doing before these 3 free days?

It sounds like you are in Japan for more time. If so, what are your other plans?

If not, then stay in Tokyo. As one day in Osaka and one day in Kyoto is not enough time to see much.

The best would be a 7-day Japan Rail Pass, costing 29,110 yen.
http://www.japanrailpass.net/en/about_jrp.html

Because your time is rather limited and I do not recommend any overnight buses, which could be much economical but lose an entire view in between such as Mt Fuji, the most reliable solution would be Shinkansen trains.

Just going and back to the Kansai area with Shinkansen costs beyond the price of 7-D JRP. Thus, it would be better to based on your plan with this pass.

With the pass, you could move among Kobe, Osaka and Kyoto with Shinkansen. It means you could just find one economical hotel in a single location. Try to find such a hotel near a JR station and sightsee with JR, though local buses and subways could be more convenient. In such case, passes in each city could be rival, but it depends on your exact location of your selected hotel.

You are travelling the last weekend in our summer school holidays. Be prepared with the crowds. On the last day, take a NEX to NRT at Shinagawa.