We discovered Tsujido Kaihin Koen about 8 weeks ago, when my son found it on one of the many maps he owns and thought it looked interesting enough to give it a try. We took the Tokaido sen from Yokohama got off at Tsujido (one stop after Fujisawa) and walked leisurely for about 30 minutes along a straight road towards the sea. It is a very beautiful, well kept park, with lots of real lawn, a flower garden, (I think),two nice, interesting playgrounds, bicycles, go-carts, etc. for free (but limited to two round of cycling) There was also a cheap sky cycle (like the ones in the yuenchis)for which we queued. Definitely the birds of prey (not sure which type) are also s.th. to watch out for and there are plenty of them. It is one of the most beautiful parks I have seen so far, and we have seen quite a few by now, and even though it was crowded, as it was sunny and a Sunday, this park is spacious enough not to feel really crowded. There was even enough space for people to fly their kites. We spent about 4 hours there, and then walked to the near-by beach all the way to Enoshima Eki, which is about 3 km, I guess. This was also quite pleasant, far enough from the street and not busy, but by then it was almost sunset, it may be much more crowded during the summer months of course. This easily makes for a one day outing and enough exercise to almost wear out even our kids, who are 6 and 10 and have all the energy I wish I had.
Here is a link in Japanese: http://www.kanagawa-park.or.jp/tujidou/index.html