Going to Mount Everest is an experience that will leave you in awe of how big everything is in the Himalaya. Sleeping at 16,000+ feet is without a doubt a highlight not to be missed when in Tibet. Make sure you are reasonably fit and spend many nights along the way to help acclimatize to the altitude. Bring a hat and gloves, as your fingers will stop working in short order when it's cold.
We hiked to Everest Base Camp a couple of years ago. You need to train for this kind of trip. Building strength in your legs and butt. Break your shoes in well and be ready to carry a small backpack. Altitude can get to you very easily. Best asset is a good guide. We used 3 Sisters and they were awesome. I wish I were young enough to do it again.