10 days....Need some serious help!

Hello people! I am planning to go to Japan in March for 10 days. I have made an attempt at an ideal itinerary but I need to if it is realistically possible to do the things on my list and if so what is the best order to do them in? I have no idea where things are or how to get to them so any help would be appreciated. Also, I am not opposed to walking almost everywhere so it would be nice to know if it is possible to walk to a lot of these sights. Can anyone offer any helpful advice for an inexperienced traveler like me? Here is my itinerary of sorts:

Day 1: Arrive in Tokyo
(it will be late afternoon when I arrive)
Day 2: Tokyo
--Tsukiji Fish market
--Sensoji Temple
--Imperial Palace and Gardens
Day 3: Kamakura
--Great Buddha
--Zeniarai Benten
--Hasedera Temple
Day 4: Mt. Fuji
Day 5:Mt. Fuji five lakes area Surrounding areas (Is the Izu peninsula a possiblity from here? Is it worth visiting?)
Day 6: Kyoto
--Sanjusangendo Shrine
--Kinkakuji Shrine
--Geisha Makeover thing
Day 7: Kyoto
--Fushimi Inari Shrine
--Kiyomizudera Shrine
Day 8: Arashiyama
--Iwatayama Monkey park
--Bamboo Groves
--Boat tour down Hozu River
Day 9: Hiroshima
--A bomb Dome
--Peace Memorial Park
--Miyajima Island
--Itsukushima Shrine
Day 10:Tokyo
--Tokyo Tower and Zojoji temple

These are the things I would ideally like to see but I have no idea if this is possible. Can anyone please help!?

If you have a whole day for Kamakura, you can cover more than just the 3 sites you'd listed. Consider Tsurugaoda Hachiman-gu and Engaku-ji, among other temples and shrines.
Zeniarai Benten is a bit tricky to get to by walking. From the JR Kamakura station, don't follow the crowd who mostly take the east exit for Tsurugaoda Hachiman-gu. Take the west exit instead, follow the main road and walk on the right. There are tiny signs that direct you to the shrine, not too notice-able though. You will pass under a road bridge, continue on the main road till you're directed to turn right onto a side-street. You still have to walk quite a bit and the last leg is an uphill climb. It takes about 20 min walk from the JR station. The entrance to the shrine is through a cave in the hill, but the shrine is small and can easily be toured in less than 30 min. including going through the "money-laundry" thing. If you're into hiking, you can hike through the mt. from here to the Daibutsu Great Buddha in another hour or so. From the Great Buddha, it's an easy 10 min. walk to Hase-dera.

Izu Peninsula deserves a few days to take in all. For just 2 days, and with Mt. Fuji included, consider just taking in nearby Hakone. Actually Hakone is ideal for a night's stay with an onsen experience and its different sites fully explored on 2 separated days - without Mt. Fuji and the Five Lakes.

Hey thanks so much for the advice about Zeniarai Benten. I had no idea what to expect with that and your advice is great. I will defintely be looking into the shrine you mentioned. I wasn't sure how much time to expect these things to take so I didn't want to plan too much but I think it sounds like a good plan to add the one you mentioned. As for Hakone, I also think that is a great suggestion. My sister lives in Yamanashi and I think that it will be close to where she is and would be more convenient. I really would like to see the beaches and coasts of Japan. I will be doing some research on Hakone. Are there any interesting sights you recommend in that area?

In Hakone, a typical route is to ride various means of transports on the popular loop course:
http://www.japan-guide.com/e/e5210.html

Places of interest along the route include Fujiya Hotel, Yunessun onsen resort, Hakone Open Air Museum, Gora Park, Venetian Glass Museum, Museum of Saint-Exupery and Little Prince, Owakudani, cruise on Lake Ashi, Hakone Checkpoint, Hakone Detached Palace Garden, Hakone Shrine, Cedar Avenue and the Old Tokaido Road.

On a clear day when Mt. Fuji is not covered by clouds (which is rare), you can have a pretty good view from the grounds of the Hakone Detached Palace, with view of Lake Ashi and the waterfront torii of the Hakone Shrine as well.

the trip you have outlined is very doable. And you will find you can see more than what you have on your schedule for each day, but good to have the flex time to see things you didn't know were there. But what I don't see on your schedule is travel times. Will you travel at night? you need to factor in your travel times to each area.

I recommend you to visit Todaiji in Nara and Osaka Castle in Osaka. You can change your plan in Kamakura to stay in Kansai area one more day or save time to trip around in Kyoto for 3 days. It takes within one hour from Kyoto to Nara and Osaka.

Well travel times are what worry me the most. I have no idea how to account for time because I have no clue about distance. I know we will be doing most long distance travel at night. I'm concerned about travel times eating up the limited time I have while there. I feel concerned about the hiroshima portion especially since it is so far. Any suggestions?

If you're travelling by train, you can work out the schedule by using this site:
http://www.hyperdia.com/cgi-english/hyperWeb.cgi

Assuming you base yourself in either Kyoto or Osaka, Hiroshima and Miyajima can be done on a day-trip, just start early.