Hotel Vista Grande Osaka is located in between Nanba and Shinsaibashi. The Hotel site says the nearest station is Nanba (for Nankai, Kintetsu, and Osaka municipal subway).
https://www.google.co.jp/maps/@34.668751,135.503185,3a,75y,355.53h,73....This is the view from somewhere near B20 exit of Nanba Walk underground shopping arcade. I do not say this hotel is located in a beautiful atmosphere, though, it is not located in a red light district. It is in a shopping/eating area in the center of Osaka. As a former Osakan, I would say it is a very Osakan place :). Nearby are Daruma, Imai, and Zuboraya which are very famous diners in Osaka.
I think you must walk about 10 min from Nankai Namba station, and using taxi might be more difficult since the road is narrow and complicated with many one-way street.
The Chikatoku ticket I mentioned earlier if useful if you take subway, but for this hotel you do not need to take subway, so you might better just by the normal ticket (Nankai line) from KIX to Namba (890 yen).
If you stay in Osaka (Umeda) area, Kansai thru pass is obviously cheaper than the normal ticket.
Osaka to KIX (240+890 yen)
Osaka to Koyasan x2 (1500x2)
Total 4130 yen
Osaka thru Pass 2 day 3800 yen
But since you are staying in Namba, the fares are
Namba to KIX (890 yen)
Namba to Koyasan (1260x2)
Total 3410 yen
However, you will use Nankai Rinkan bus in Koyasan.
Koyasan to Okunoin 330 yen
Okunoiu to Koyasan 330 yen
Further, you might want to ride the subway on the last day.
Then I think still Kansai thru pass has advantage to the normal tickets. It should be mentioned that if you have the pass, you do not need to buy the tickets each time.
Have a nice trip in Osaka!