I am visiting Osaka first time and was recommended to stay in Namba district. I am a fan of onsen. Are there any good hotels with onsen in Namba district ?

Am fairly sure the answer is no (because of Osaka's geology, in a basin/plain, I think).

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I visited there for a soak but there is quite a bit more to it, including hotel. It is about a mile from Namba station, but there might be a closer station. Call it Namba-adjacent if not in Namba. They say they have an onsen, but I have my doubts that the water is actually from a hot spring. That would be ok with me because am not a believer that the various minerals in natural hot springs water have any therapeutic benefits, but maybe there is some temporary skin benefit. [reminds me of a remote onsen in Tohoku that has some radioactive properties, in the rocks IIRC, and I decided not to go because my fellow bathers would be cancer patients/sufferers]

There is an "Onsen Bus" from Osaka Station to Arima Onsen. The schedule allows for a day trip which might be its primary purpose. Or it is secondary to use by Osaka-jin for an overnight getaway to an onsen ryokan. As you may know, Arima Onsen is the real thing. It is, unfortunately, still on my onsen wish list.