You could always just look for someone's house that has a great garden. Ask the home owner, I doubt they would have a problem. Offer them some pics that you shoot.
Whitehall has always been a fabulous place. But they are now charging high fees to allow you to come and photograph there. Have you thought about Gardencourt? On the Presbyterian Seminary property?
Also try Bernheim Forest. But I imagine just about any well kept garden will do. Anyway, some of the most interesting advice I ever got about photographing butterflies was to shoot early in the day within about an hour of sunrise. The time when the grass is still wet with dew. That's because butterflies' wings are wet too. They're more likely to just sit there (drying out in the sunlight) as you get close with a macro lens on a tripod mounted camera . That's also the best light in which to shoot flowers.