Don't be fooled by the word 'Cemetery.' Lakeview Cemetery is really a beautiful park, that also happens to contain some grave markers. It's often so full of joggers and sight seers that you could mistake it for a stunning sculpture garden.
The view from the top of Garfield Monument is one of the best from the east side.
Also check out a small temple decorated by Lewis Tiffany. Every surface is covered in mosaics. Often, you can get a guided tour by flashlight. Not his most breathtaking work, but beautiful nonetheless.
Be careful. The gates close at 5PM, and it's possible to get stuck on the wrong side(!).