If you have a JR rail pass, staying in Osaka and taking day trips via the Shinkansen is a fantastic way of organizing things. They're close enough that moving all your stuff from hotel to hotel isn't really worth the convenience of being closer (espcially Kyoto, but Hiroshima is only about 80 minutes away). I spent 5 days in Osaka last summer and took a number of day trips to the surrounding cities.

There's lots to do in Osaka, but it depends on your interests. If you have kids, there's a fantastic aquarium (and optional harbor cruise, which is worth checking out) and some castle museum parks—really depends on what you're interested in though.