Perhaps the best onsen close to Osaka, Arima Onsen offers two main baths -- Kin no Yu (Gold Bath, 金の湯) and Gin no Yu (Silver Bath, 銀の湯). Kin no Yu has nice, hot rusty ochre water due to a high concentration of iron and other minerals; whereas Gin no Yu has water of a more unusual type: Radium. Though locals will swear by its healing powers, treat Gin no Yu (like all onsen!) with some respect, and decide for yourself whether you're up for self-dosing with radiation therapy. Both baths are public and are open from morning to nine or so at night, however they close certain days of the week, so ask at your hotel prior to making plans.
Arima Onsen is easily accessible from Osaka by train, but an inexpensive bus runs direct from Osaka Station as well, giving travellers easy access -- either way, you'll need at least an hour and a half. Once there, you'll find that the town is small and fun to walk around in. Stairways lit with lanterns and several beautiful temples make night strolls fun, and the town is big enough to have a selection of restaurants, shops, and convenience stores.