There isn't much around the park. Hotels in the district itself will probably be more expensive than in the surrounding area. I'd look either in Arlington or Alexandria, either Old Town or Crystal City especially; those areas are just as easily accessible to the Metro.
Let me know if you have any other questions about DC, I lived there for 2 years.
09 : 3-2.
10 : 2-3.
12: 2-1; Orlando Hudson and Alex Rios walkoffs.