Osaka has an extensive public transportation system that includes buses, trains, and subways. The easiest and cheapest way to get around is by purchasing an ICOCA card, a rechargeable smart card that can be used on all forms of public transportation. Day trip destinations like Kyoto, Nara, and Hiroshima are easily accessible by train from Osaka.
If you have more time, consider adding a day trip to Kobe to try the famous Kobe beef, or exploring the charming Takayama in the Japanese Alps. If you have less time, consider cutting out the day trip to Hiroshima and spending more time in Osaka.