Might look into International Village Apartments. Don't know much about them but believe take pets. I go to church with the developer that owns these. He seems okay. Its on south side near mall.
Cobblestone Crossing is a little south of TH and is new (<3yrs). Big complex. Don't have a clue about $$ or pets. Lots of amenities I hear.
Also, might contact Robinson Rentals (812) 235-9353. Used to work with the owner. He was a good guy. Don't have a clue about his apartments though.
If you get this way and want a place to shoot, come with me to check out the Riley Conservation Club. All outdoors for $70/year. Believe there are 5 bays for pistols and also range for long guns from 25yds to about 225 yds. Host rimfire & steel challenges, plus IDPA and USPSA regularly.
Thanks a lot. The conservation club might be right up my alley. I'm a member of the Elwood one and love it. I'll let you know once everything is settled.