Osaka is not that great of a sightseeing city, so a visitor can easily get a good sense of it in just one day or less.
Here's a suggested itinerary for spending the day visiting the main sights of Osaka:
1. Start by visiting Osaka Castle for a couple of hours (600 yen) in the morning. Take the time to check the interesting museum inside displaying samurai weapons & armor. (It would be possible to visit the Tenjimbashi-suji shopping street at this point as well.)
2. Catch a taxi (easiest) to Shi-Tennoji Temple (only 5-10 min., costs around 1000 yen) and walk around there (mostly free) for an hour or so. This is the main Buddhist temple of Osaka. (It is also possible to take the purple Tanimachi subway line there to Shi-tennoji-mae-yuhigaoka station from Temmabashi station near the castle.)
"The oldest officially administered temple in Japan, Shitennoji was
built by Prince Shotoku (574-622 A.D.), the great cultural hero of
early Japanese history who at the age of sixteen successfully triumphed
over the opposition and brought about the adoption of Buddhism in the
country." --Osaka Tourist website
3. Walk south (downhill) for about 10-15 min. to Tennoji station (very easy to find this huge station complex), observing the typical Osaka streets & stores along the way.
4. At Tennoji station, visit the B1 basement food floor of Kintetsu Department Store for a very interesting mini culinary tour. Don't be too shy to try the free samples.....that's why they're offered! (If not here, then a similar visit is possible at the B1 food floor of Takashimaya Dept. Store in Namba station.)
5. Catch the Hankai line trolley car from Tennoji to Sumiyoshi-Taisha Shrine
(takes 15 min., pay 200 yen when you get off, not on). This is the main
Shinto Shrine of Osaka, and is amazingly quiet & peaceful like a Zen garden. Cross the famous Taiko-bashi Bridge and wander the shrine grounds (free) for an hour or so -- you are likely to be the only tourist there. Gates close at 5pm. The trolley line is one of the last still functioning in Osaka, and a ride on it is like a time machine through 1950s Japan!
"Osaka’s most famous shrine by far is Sumiyoshitaisha (Sumiyoshi Grand
Shrine), the headquarters of some 2000 Sumiyoshi shrines throughout
Japan. It enshrines three gods that have long been worshiped for
protecting the nation, for protecting sea voyages and for promoting
waka (31-syllable) poetry." --Osaka Tourist website
Also, at Sumiyoshi Taisha station, don't miss a walk through the covered shopping street ("sho-ten-gai" in Japanese) for an interesting look at how the locals live & shop. It has a nice "old Japan" feel to it, in contrast to the modern hustle & bustle of Namba. You could (and should) even walk all the way to the next station (called Kohama, about 10 minutes walk) and then jump on the local train for the short ride to Namba.
6. Catch the Nankai line train from either Sumiyoshi-Taisha or Kohama station to Namba (200 yen, 10 min.) and walk around the famous Dotombori/Shinsaibashi shopping area for a couple of hours. See the fashions (check out the sales girls for how to wear the latest combos!), eat some famous Osaka tako-yaki from a food stall, see the neon lights in the evening (especially the famous Glico running man lights).
- Computer or other tech geeks would want to check out the nearby Den-Den Town electronics district, which closes at 7 pm.
- For underground/street fashion & shops, head over to the nearby America-mura zone around Triangle Park.
- You can even quickly check your email for free as you "shop" the latest Macs at the Apple Store right there on Midosuji boulevard!
- People watchers will want to hang out on the Dotombori bridge and watch the throngs of Osaka pass by.
7. Enjoy a nice (but relatively cheap) Japanese dinner in the area and see why Osaka is known as both a frugal city AND the culinary capital of Japan. Those with energy for nightlife in Osaka will find no shortage of it with all the bars & clubs in the area. Check the forums for details & suggestions.
And that, basically, is how to enjoy Osaka in Single Day!