Ueno Park is free to enter and has plenty of shrines and temples to enjoy.
Tucked away in the corner near coffee shop after the entrance is a wonderful service that you should take advantage of.
Tokyo SGG Club (Tokyo Systematized Goodwill Guide Club) offers a free guided walking tour in English led by a volunteer. Luckily, I was the only one who show up that day, so I got not only free but also a private 90 minute walking tour. This kind and informative volunteer was a retire military man who was stationed aboard. He told me that he does this , so he can keep practice English. He was eager to explain the Japanese culture and history, the difference between a temple and a shrine. the history of Ueno area, and the important places in the park. He taught me how to pray, step by step and remind me that the water well in front of the shrine is to wash the hands, not to drink. :-)
The tour is offered every Sunday, Wednesday and Friday. The tour departs twice a day at 10:30 a.m. and 1:30 p.m. Get there 10 minutes before departure time.
Tokyo SGG Club also offers the same service in Asasuka, and Imperial Palace East Garden