For your first day, A great trip plan to osaka is:
Try the following places in this order.
-Osaka Aquarium (Kaiyukan)
-Tempozan Marketplace (Naniwa Kuishinbo Yokocho, a food theme arcade)
-Tempozan Giant Ferris Wheel Grand front Building/Hankyu (for some shopping)
-Umeda Sky Building (at sunset time)
-Dotonbori and Namba
And for your second day:
-Osaka castle
-Kuromon Market
-Tennoji Park
-Tsutenkaku Tower and
-Shin-Sekai area Abeno Harukas