Summary
Saitama is a nice place. Like just friggin' nice. When Tokyo is stressing you out, get to Saitama. You'll feel nice. Also Crayon Shin-chan lives there.
Hikawa Shrine is one of the most important and oldest shrines in Japan, dating back 2000 years. Train nerds will have trouble leaving the Railway Museum (closes at 6:00pm). Omiya park is actually three parks featuring a zoo, swimming pool, amusement park, museum, and archery grounds. Not sure when you have to leave there.
Get to Saitama and get nice.