Hyde Park is a beautiful park to walk through, and also as pleasant a spot as any to spend an hour or two. With its center walkway lined with benches and magnificently tall trees you can do a little of both. There's nice flowerbeds and gardens throughout the park as well. And as you're walking you can look up and see the skyscrapers towering right above you.
This park takes on further importance, particularly to Australians, due to the fact that it contains some impressive and important war monuments.
At the north end of the park is the Archibald Fountain, built to commemorate the association of France and Australia during World War I. In fact this fountain wouldn't look out of place in any major European city, and it looks quite nice here too. Nearby is a giant chess set, which can be a fun way to pass time.
More towards the middle of the park is the Sandringham Memorial Gardens, which commemorate Australia's war dead. Again very nice, and worth a look.
But the most impressive of all the memorials (even if I'm kind of partial to the fountain) is the ANZAC Memorial at the south end of the park. A tree lined pool of remembrance fronts the 30 meter high cenotaph. It was unveiled in 1934 and is classic Art Deco. Check out the stylized soldier fingers decorating the inside. You may not know what "ANZAC" means or anything about Australia's war history, but you will learn about both if you walk through the memorial/museum inside.
Please keep in mind that even if the significance of this memorial doesn't hit you, it is very significant to Australians. Therefore it's no place to be loud, obnoxious, or horsing around. Instead take it in. It's one of those special places a country has where people come to not only remember their war heroes, but also to remember how horrific war is. You can't help but be slightly impressed by it all.
If taking the train get off at St. James station for the Archibald Fountain end of the park, or Museum for the ANZAC Memorial end of the park.