I love this place: http://www.indyarts.org/
I got my IndyArts card in the mail today, too. Now, not only can I find a database of artists (of all kinds), search calendars, apply for Arts Council grants, find out about the hundreds of FREE events at the ArtsGarden (an incredible seven-story glass enclosure connecting hotels, shops, restaurants and the convention center), I can also get discounts and e-mail newsletters.
One thing you cannot complain about in Indianapolis is the city's dedication to its artists and art organizations. The Council has a new site as well: PAL or Public Art Locator, which pinpoints public art exhibitions on a map of the city.
I feel so artsy.