Having had been an Osaka resident and not a traveller to this great city, I can’t really speak a lot on accommodation. I stayed in one small hostel in a quiet residential area that is still close to the action called Hostel 64 Osaka, which I would highly recommend for its location, comfy beds, chic decor, and seated showers (you gotta try it out!)
So while I can’t really speak about many specific places, I can let you know what neighborhoods I recommend and sometimes more importantly, what subway lines to stay on for maximum convenience. Unlike Tokyo and its scores of neighborhoods spread far and wide, Osaka is pretty much split between Kita (Japanese for north) and Minami (Japanese for- you guessed it- south)
The hub of the north part of central Osaka is the gigantic Osaka/Umeda train station that home to not only the JR trains, but also the Hankyu and Hanshin train lines and three very convenient subway lines(Midosuji, Yotsubashi, and Tanimachi). The station itself is a destination, especially if you love to shop. It is connected to floors upon floors of boutiques and two major department stores that always have the most beautiful storefronts, regardless of the season. This area is also surrounded by plenty of business offices and wherever you find salarymen, you will find a wealth of eating and drinking establishments. This area can be a bit overwhelming and confusing, but a five minute walk away from the station in any direction will bring you to a quiet neighborhood. One of my favorite quiet neighborhoods in this area is Nakazaki-cho, a quiet area with lots of local shops and cafes.
If you want to look at Kita-ku as the “Uptown” part of Osaka, then Minami-ku would definitely fit as its “Downtown” counterpart. While there are many drinking and eating establishments around Umeda, it does not hold up compared to the options you have down here in the neighborhoods of Namba, Dotombori Shinsaibashi, and Ame-mura. These four neighborhoods blend together and can provide hours of entertainment just walking through them. I am personally biased to this area of town as I lived here for two years, in a quiet neighborhood just north of Ame-mura called Shinmachi. I personally liked this area over Kita-ku because for me, it just seemed a lot more “real Osaka”. Sure, there are many tourists in the area, but stroll a few minutes off the main drags and you come across countless numbers of locally owned bars and restaurants filled with friendly and raucous Osakans ready to kanpai (cheers!) with you over a beer. While I would not recommend staying in the area (although you can find a few hotels and hostels in these neighborhoods) I’d highly recommend staying in a neighborhood right along the edges of this district. Neighborhoods like Kita Horie, Minami Horie, Shinmachi, and Minamisenba.
Unlike in Tokyo, the JR train lines in Osaka do not connect any areas of town that you would want to go to. More convenient for travel around town are the subways. The Midosuji, Yotsubashi, and Tanimachi lines will take you almost anywhere you need to go from north to south. For east to west travel, the Nagahori-Tsurumi Ryokuchi Line is convenient as it goes between Osaka Castle and the Shinsaibashi/Namba area. If you don’t find a place close to any of those lines, look for a place that is close to a line that you can transfer to one of those lines.