Imperial Palace East Gardens

I read on the site that Imperial Palace East Gardens " are a part of the inner palace area and are open to the public". So this means that is part of the Imperial Palace tour that needs advance booking or is it a separate thing?

Separate. There is an entry gate and free admission - you get a token that you return so they know if anyone is in the grounds at the end of the day.

Regarding tours of the Imperial Palace, this recent development might be of interest to you:

http://www.kunaicho.go.jp/e-event/toujitsu-sankan-start.html

If you're only planning to see the East Garden...

https://animeaffairs.wordpress.com/2009/04/21/japan-2009-day-2-report-...

...then no prior arrangements are required.

Cheers.

About Imperial Palace, I'm not interested in a tour inside because it seems not worthy for me. What do you think?
Where can I find pics of what is included in the tour?

If you are not interested, why go? It (a view of the palace/moat wall) is not a particularly good tourist spot (brutal truth), but something easily added to a bus tour (maybe because they have parking).

The tour goes into the heart, the west part of the Imperial Place, the prohibited area where the Emperor lives and works. The east garden, the former Edo castle, is in the east and opens to the general public.

http://www.kunaicho.go.jp/e-event/pdf/sankan-annai.pdf

Where can I find pics of what is included in the tour?

This is a rather old post I wrote about my experience:

https://animeaffairs.wordpress.com/2009/04/13/japan-2009-day-2-report-...

Truth be told, I wouldn't recommend the tour to most casual visitors because there's not all that much to see. You're not allowed inside any of the palace buildings, which are themselves pretty drab and modern on the outside. I personally thought it was well worth my time (indeed I might go again at some point), but that's because I have a rather obsessive interest in Japanese castle architecture - there are a number of features of the former Edo Castle that are best appreciated from within the restricted area. On the other hand, I wouldn't be surprised if many other people might find the experience a trifle boring.

Cheers.