The Onsen (hot spring) has a special place in Japanese culture. There are books, magazines, and package tours centered around Onsen, and it is the premiere way to relax in a society where words like "gaman" (endure/bear) and "ganbaru" (strive your hardest) are heard almost daily by everyone in the society from the time they enter preschool until the time they retire. Relax, like Enjoy and Work, are state-of-mind verbs in Japan, meaning they are to a certain degree decided upon states of being, often aided by props (the tie around the neck during Work, the tie around the head for afterwork Play.
While numerous cheap (¥300) public baths pepper lower-income neighborhoods in Osaka (in the past apartments came equipped with toilets but no bathrooms), Spa World (Japanese language web site - http://www.spaworld.co.jp) sets itself apart with deep, well-accessed natural hot spring water and fantastic themed settings. The hot springs themselves are divided into two main "zones", Asia (including Islamic, Persian, Chinese, Japanese Hinoki wood bath, Indian, Japanese outdoor bath, and a "Japanese Rest" area), and Europe (including Roman, French, Greek, Finnish, Spanish, German, and "Grotta Azzurra" blue cave bath). The themed baths are well done in a kind of Vegas style with landscape murals on the walls or starry nights painted on the ceilings in the "outdoor" settings, all of which adds to the fun. If giving the subtle sensation that you are sitting in an exhibit at the Natural History Museum (non-Asian foreigners can get stared at a bit in Japanese public baths and traditional onsen, but thematically speaking they should fit right in the Islamic or European "Zones" here).
There is also an excellent gym/fitness facility available and a kid-oriented swimming pool with waterslides and fountains. Note: the 'Rules' at Spa World say "No Tattoos", though this is a common roundabout way of reserving the right to refuse service to Yakuza. It is much easier to say "sorry kind sir, no tattoos allowed" than "sorry no gangsters here". Foreigners with tattoos, as long as they don't resemble the large traditional Japanese tattoos, will not be asked to leave.
Spa World is a bit of a splurge. Bathing with a three hour time limit is ¥2,400 adult/weekdays ¥2,700 adult/weekends and children under 12 are ¥1,300/1,500 respectively. Spa World does offer accommodation and can be a good option for a night or two, as the prices include use of all baths and recreation facilities. The rates range from ¥16,000/night up to ¥54,000 per night, though the scale is complex depending on the number of people, weekday, weekend, Japese-style room, and Western-style room. A good family option could be the Japanese-style room, sleeping four people for ¥20,000.
Festival Gate (Japanese language web site http://www.festivalgate.co.jp) is, along with Spa World, one of the new developments in the rejuvination effort of the long-neglected Tennoji neighborhood. It's a family-friendly, clean amusement park surrounded by what is otherwise one of the few "rough" neighborhoods Osaka has to offer (it isn't dangerous by American standards). There is enough here to keep both kids and adults entertained, and Spa World is just across the way if you need to chill afterwards.
Festival Gate is clean and compact compared with the sprawling amusement parks found in places like southern California, all squeezed into eight floors of fun. Highlights include Sega World (video games you won't see outside Japan for a few years), Delphin Arena (a local Osaka pro-wrestling arena where matches are held on the weekends--call 06-6635-1100 for details), Bridge (a non-commercial alternative music space--call 06-6634-0080 for details), Dios Fall (a 45 meter free fall ride, ¥500), and Delpis The Coaster (roller coaster,¥ 700).
There are also a number of restaurants in the complex, including Italian (where you can get the Japanese favorite spaghetti with salmon roe), gelato, various cafes, donburi (usually called "rice bowls" in English), and the Japanese fast food hamburger chain Mos Burger (see menu here, view diagram of Mos Cheese Burger here), far superior to its American counterparts, my favorite eating place at Festival Gate, and a must-try for any visitor to Japan (a country-wide chain, don't make a special trip to Festival Gate).
Spa World and Festival Gate are a five minute walk from the Doubutsuenmai station on the red Midosuji subway line, or a 10 minute walk from JR Osaka Loop Line Tennoji station.