Best places to hunt doves ?

Glad you're excited-PCPs were definitely a game changer for me!
As far as dove hunting, first make sure it's legal to take the Mourning doves with an airgun (it's not in California). The two most common doves aside from pigeons are Mourning doves and Eurasian collared doves. The Collared doves are seen around ag and urban areas and are considered invasive pests. In some places there's no limit and season is open all year. The native Mourning doves will be around ag operations as well such as feed lots, pastures and grain stubble. All doves need to drink so look near water, especially morning and evening. As in any kind of hunting, grab a pair of binoculars, put on your walking shoes and get out there! Pay attention to places that hold game and note the times of day they're usually around, can't really get more specific than that.

PS-a rangefinder is huge help as judging distance can be tricky, make sure you know your trajectory so you can place your shots well. Avoid the bend of the wing, it acts like a kevlar vest. A bird with a broken wing will dive into cover and be very difficult to retrieve.
Shoot safe,
John

You can't even hunt the eurasian collared doves? blasted thing are all over my area in eastern washington. My neighbour and I have an informal contest to see who can get the most.

Season for Eurasian Collared dove in Indiana is year round for residents. I think if you talk to a Game Warden you may find that in the case of the Eurasian Dove you can hunt with a air rifle. Pigeons too I would bet. Hunt them near grain storage or harvesting areas for best meat. 

Thurmond

I like to filet the breast, rub with olive oil, salt and pepper both sides. Cook on a very slow fire, you know it's right if it takes 15-20 minutes to cook.

Spikes,
It's been about 6 years since I have lived in Indiana, not sure if the Collared Doves have made it that far north in the Midwest yet. As of 2008, I had never seen a collared dove in Northern Indiana and I have done a lot of dove hunting there.

There are alot of Silos with pigeons on them in Indiana. I would be checking with farmers seeing if they needed help getting rid of all the pest pooping in their grain bins. Also alot of starlings, one of Ted's favorite targets. Although I have never hunted them, I believe you can hunt ground hogs with an air rifle as well.
It does suck that you can't shoot mourning doves with an air rifle and it is highly likely that the law will not change. Migratory birds are regulated at the Federal level so I believe it would take an act of congress to change the law. Not very likely.

Squirrel season opens up this month. I used to hunt a farm down near Willow Slough for the large Fox squirrels. There a few animals in Indiana to keep you busy!

Squirrel season starts in the 15th of August. After that its a month or two before rabbit season opens. I'm pretty sure I've see collared doves in the south along the Ohio river. Not many, but worth taking down if you do pest control for a farm or two.