New to Cleveland

I'm a new grad from the U of Iowa that was just offered a job at the Clinic on the Heart/Lung Transplant Unit. I'm super excited to get started in the next month, but the idea of moving to a city that I've never been too is kind of freaking me out!!!

What are the best areas to live in for a young adult/new grad? Most importantly, I'd like to live in a safer area with the shortest commute possible! I've been riding my bike almost everywhere for the past 5 years, is this possible around Cleveland? I would like to live relatively close to the Clinic and have been looking mostly at downtown, Cleveland Heights, and Shaker Heights. Let me know if I'm headed in the right direction!!