IMO the drive to Talkeetna is pretty boring, although if the weather's good you can get some glimpses of Denali here and there.
My first pick for a day trip would be Independence Mine and Hatcher Pass, in the mountains behind Palmer. In June there might still be some snow on the ground here and there (depends) but the scenery is always spectacular and the history is very interesting. You might also drive up the Knik River Road on the way back; there are frequently moose, and sometimes some black bear, around the road. Stop at the Eklutna Tailrace on the way back to see if there are any king salmon being caught, and definitely stop at the Native village of Eklutna, with the colorful "spirit houses" covering the graves in the cemetery next to the Russian churches. Map -
https://goo.gl/maps/sKUAw6bX2Lx
Hatcher Pass/Independence Mine -
Knik River Valley
Eklutna Tailrace
Eklutna cemetery
