How big of a pot are they in. I would have planted in the ground if I could.

The question of which side of the porch depends on whether the bottom of the pot will be in sun. Peonies will live in pots but the summer sun will cook the root if the pots are exposed to the sun especially during the heat of the day.

Well, everything I've read has said to not plant peonies in summer, but wait 'till fall. Hence my hesitation.

The pot is a pretty decent size (it used up about half my bag of soil to fill!). I guess I'm just not sure where to put it, period, since it can't be perfectly happy in the basement, large windows or not. Can I put it out on the back porch (morning sun) and cover it if the weather gets too cold or there's a frost?

Sounds good to me. Go ahead and put it on the porch. Planting the roots in pots this year is a good idea and they should be ready for the garden in the fall. Al

I grow all my tree peony in pots with diameter from 40 to 60 cm. I've 7 of them. The oldest one is the 4 years old High Noon with 11 buds this year.