Lincoln Park is an EXTREMELY family friendly neighborhood. It boasts one of the top elementary schools in the state, Lincoln Elementary, and is full of different parks and playgrounds for children to play in. My favorite is Oz Park, located at the intersection of Lincoln and Webster. Check out the various "Wizard of Oz" statues...very cool!
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You need to check with the local police department for crime statistics. You can also find them on line. You might feel more comfortable starting out in a high rise building as they usually have 24 hr doormen etc. I can send you some listings if you like. Please contact me via my web site.