According to the National Park Service, Meridian Hill Park was designated as a National Historic Landmark in 1994, as "an outstanding example of early 20th-century Neoclassicist design in the United States." The design is Italian (lots of wide open stone, or "hard" spaces and some statues and water feature). I don't know about all that, but I know I really enjoyed walking around this park on a sunny May morning.
My son and I entered the park from the north, which is basically a wide open area where it seems all the locals bring their large dogs to do their business and not clean up after them. And like many parks in the District, there are some homeless people who make their beds here at night. Once you get to the fountain area all that changes.
If there was any doubt about the Italian influence on this park you have to look no farther than the statue of Dante (yes, that Dante).
There is a lot of Washington, D.C. history in this park, or the land it sits on, but I think even if you don't care to know all that, you can really enjoy this park about any time of year, just being still and listening to the water fall down the cascading fountain.
To look at some of the historical photos of the making of this park (and they are worth looking at), go here.