One of the most popular attraction spots in Tokyo is Yoyogi Park, located near Shibuya and Omotesando. Shibuya is a fashionable area popular among young people, on the other hand Omotedando is a more upmarket. Unfortunately, Japan lacks greenery and parks something that is abundant in the UK. Walking down a high street here in Tokyo it is not uncommon to walk a kilometer without seeing a tree in sight.
Yoyogi park is really nothing special especially when compared to Hyde Park in London. It is wide and spacious but it looks more like a camping site than a park. On a sunny weekend Yoyogi Park tends to be very busy attracting a lot of people including many tourists and foreigners. Yoyogi park perhaps has too many foreigners and tourists which reminds me that I am myself one. For this reason I prefer not to go to Yoyogi Park.
Surprisingly some parks you have to pay to enter such as Shinjukugyoenmae. Overall if you're in the area it's worth visiting at least once but I prefer to visit small local parks which tend to be better maintained and less of a touristy feel.
Yoyogi Park is a huge and lively park in Tokyo. It is free to enter, so you get all kinds of people there.
It is close to Harajuku station, so you can see the famous Japanese kids who where gothic clothes, 'cosply' people who base their fashion on Japanese animation characters and the famous rockabillies (Japanese rock and roll dancers with Elvis quiffs). A lot of aspiring musicians perform at the side of the park as well.
It is best to visit the park on weekends as this is when the fashion kids are away from school.
The atmosphere in the park used to be a lot better 5 years ago, but now it is full of tourists. As such, the fashion kids have become shy and have moved to other areas of Tokyo.
If you are not familiar with Tokyo, I recommend exploring the crowded Harajuku area first, move to the tranquil Meiji Shrine and then go to Yoyogi Park for a picnic.