I just rented a home in that area that I have managed for close to two years and I have never had an issue. The neighbors are friendly and (in our case) despite being relatively close to the old water and sewer offices and elementary school the traffic is quite minimal.
Hope that was helpful. You may want to check with the City of Miami's website for crime statistics from the Police dept. I believe you can get this online.
Southwest Grove is a beautiful place to live. We just sold a house there and met many of the neighbors. They are very friendly and community oriented. Let us know if you need help finding your dream home.