There is a relatively new botanical garden (White River Gardens?) at the Indianapolis Zoo. You could contact Lori Johnson-Roedell for more information. (ljohnson@indyzoo.com)

Plus the zoo, itself, is well planted and of horticultural interest, including a desert biome under glass.

I enjoyed the White River Gardens at the zoo. I don't really know of any other public gardens in the area at all.

White River Gardens is very nice but fairly small. Even wandering through with a horticulture friend, where we stopped often and studied plants and design, we did the whole thing in fairly short time (I want to say not much over an hour). A good choice if you're downtown and don't have lots of time.

The grounds at the Indianapolis Museum of Art are also very nice (and free). If you want to read more, go to the link below and click on the link for "Oldfields -- Lilly House and Gardens" and then the link for "Gardens and Grounds." There are links for the various specific gardens from there. The gardens, which were designed by the famous Olmsted Brothers firm and neglected (really, lost) for many years, were rebuilt and planted not too long ago -- I want to say about 10 years ago but I don't remember. They're really lovely now. A lot of the acreage isn't heavily planted but it's a nice place to go to get out of the city racket and the gardens near the house are quite nice. And if you have time and are interested, the museum has some good exhibits. The drawback is that the museum is out on 38th St., not downtown, so depending on where you're staying it might not be convenient.

For whatever reason, Indy is really short on gardens. Too bad -- more of that would be a nice addition to the city.

Enjoy your trip!

sorry -- I forgot to add the link! Here it is, below....

Here is a link that might be useful: Indy Museum of Art

I know it's been a while since you posted your question but hopefully you're still looking at replies. I urge you to go to the Indianapolis Museum of Art for the most stunning public garden in Indianapolis. I don't know whether there is public transportation to the Museum, but it is well worth the price of cab fare to see these gardens. It's about 4 miles from downtown and admission to the garden is free. The Museum has been closed for several months as part of a giant expansion project and will reopen on May 7th BUT... the 26 acres of gardens and the Lilly House (which is on the National Historic Register) have remained open and are not to be missed. There are public tours at 1:00 pm on Saturdays and Sundays, departing from the Lilly House. The gardens feature a formal garden, a ravine garden (designed by Percy Gallagher, a member of the Olmstead Brothers firm), a grand allee which is flanked by two border gardens and a greenhouse. Many local gardeners don't realize what a treasure this property is. I'd be happy to answer any questions.

I know this is June but for any other visiting Indianapolis there is:

Here is a link that might be useful: Garfield Park and Conservatory