I did not go last year, but I went the year before and the year before that. We had a time around 12:00, I think and we just parked at a parking garage around the area. There are a lot of garages. They are around $20 to park, but it was worth it for me. We had to walk about a quarter of a mile. By the time you pay for parking at the Metro, then the Metro, it wasn't worth it for me. I'm not a huge fan of the Metro in general.
It was fun to go, but my friends who went last year said it wasn't nearly as organized or fun as the years before. Hopefully the Obamas worked out the first year kinks. Would I drive 3 hours and pay for a hotel? No. But it's something you need to experience for yourself to see if it's worth it. If the weather is anything like it's been today and for the weekend, then it'll make the experience more enjoyable! When I went it was pretty cold.
It's not an egg hunt; at least the 2 years I went there was no hunting for eggs. The main activity is rolling an egg they provide for you across the lawn with a spoon. Then on your way out, you usually get a bag that has a commemorative wooden egg. Last year they did not provide food, so I would eat something before and bring some fruit snacks or pretzels. They say no food, but nobody said anything when I brought it when they saw the ages of my kids. The worst they can do is trash it at the entrance.