KL is a very integrated city, and Malays, Chinese and Indians all seem to share the same neighborhoods (along with ex-pats from western countries). I lived in Brickfields, which has a large Tamil population, a few Chinese and a small minority of Malays. It's a nice neighborhood - as Indians, you'd fit right in. It's very convenient to public transport, too, and there are some excellent restaurants in the area and a great little Indian night market. To find a place, either check the paper (The Star or the New Straits Times are the two main newspapers for KL) or find some agents through Malaysia Property & Real Estate For Sale / Rent - iProperty, and browse through the rental listings for that area. Villa Scott, Scott Sentral and Palm Court are three big condominiums in Brickfields, and there are several smaller ones, as well.

You might also find some nice areas in Bangsar, Petaling Jaya or Klang (which is further out). Keep in mind that most leases require at least a 6 month commitment and most landlords want to have a one year lease. Expect to pay first month, one month security deposit, a utility deposit and the stamp fee. If there are no damages or delinquent rent and you stay for the duration of your lease, all money other than your normal rent should be returned when you vacate except for the stamp fee, which will be somewhere around 300-400 RM.

Hope that helps. It's a neat city - I'm sure that you'll enjoy it!