I recently moved from Lincoln Park and it's not one of my favorites in the city. It's a bit overcrowded with students, which is fine if you're in that age range. I completely agree with Lakeview being a great area and would add the Bucktown area as well.
Definitely Lincoln Park or Lakeview. Lincoln Park is much more expensive. Both have a ton of young people living there. The majority of shops, bars and restaurants cater to and attract young, single people too - more so in Lakeview. They're both safe and there's plenty to do.
