Tsutenkaku Tower
Tsutenkaku is open all year-round from 10am - 6pm. Their phone number is 06-6641-9555. Entrance is 600 yen. Kids under 4 are free. From the 103 meter high tower, you can see most of the Osaka/Sakai area. Directions: Get off of either the Midosuji Subway line at Dobutsuenmae station or the Sakasuji line at the Ebisucho station. Look up. Find the big tower. Walk toward it.
Festival Gate
I've heard mixed opinions on Festival Gate. Some people say it's dangerous because there are strange people walking around. But I saw a ton of security guards walking around the three times I went there. The best things about Festival Gate is that it is close to Namba, it has a not-too-bad roller-coaster (700 yen), and there is no entrance fee. So in the evening, it's nice for a romantic hour or two; eating food at some decent restaurants, shopping, playing video games and taking a ride or two. If you live here, and find yourself spending every weekend wandering around Namba, get on the subway and go to Festival Gate for a bit. I can't recommend it if you are a tourist. I mean, this place ain't Disneyland. Directions: Take either the Midosuji or Sakaisuju subway line to the Dobustuenmae Station and follow the signs. OR Take the JR Loop line to Shin-Imamiya, and you'll hear the roller-coaster and see Festival Gate, east of the station.
Tennoji Park
1300 kind of animals live in the Tennoji Zoo. Also in the park are the Osaka Municipal Museum of Art, and lots of greenery and flowers. Take either the JR Line, the Midosuji line, or the Tanimachi line to the Tennoji station. Or take the Kintetsu line to Abenobashi. Art Musuem phone 06-6771-4874. Zoo phone 06-6771-8401. Last admission to the zoo is 4pm. Admission is 350 yen, free for Jr. High students and seniors.