Itinerary help - 13 days in September

First time traveling to Japan and will be traveling with my partner. We have booked flights but have not yet booked the accommodation.

Intending to use Osaka and Tokyo as a base to travel the region. Not sure if have put too much or too little into the daily plans. Any suggestions on changes to the itinerary or additional places to visit (particularly around Tokyo) would be appreciated. Also very interested in any particular activities that other people have founds to be highlights in Japan and any restaurant recommendations.

Japan trip itinerary
Day 1 Osaka
Arrive Osaka airport 9pm
Travel to accommodation
Dinner Osaka around accommodation
Sleep

Day 2 Osaka
Morning
Osaka Castle and grounds (or just grounds) - 2 hours
Osaka museum - 1.5 hours [1200-1330]
Afternoon
Namba district
-visit shinsaibashi arcade
-visit amerikamura
-visit dotonbori after dark
-if time can visit namba parks
-Dinner around dotonbori
Return to accommodation

Day 3 Osaka
Morning
Umeda (Kita) area
-Shopping in osaka station
-Visit Grand front osaka
-Visit HEP FIVE
Get lunch in Kitashinchi district
If feeling up to it and there is time - can see Tenjinbashi-suji street (2km street) +/- nearby osaka tenmangu shrine
Afternoon
Travel to Shinsekai to explore area
Dinner in shinsekai district
Spa world after dinner

Day 4 Osaka - Day trip to NARA
Wake up, check out, breakfast in Osaka (~10A)
Arrive JR Osaka station - Train to Nara - Arrive ~1130
Walk 30 minutes to Park - arrive ~1230
Explore park and below attractions for 4 hours or so
-Todaiji Temple, Nandaimon Gate, Nara park, Todaiji museum, Kasuga Taisha, Isuien garden.
Return to Osaka for dinner

Day 5 Osaka - Day trip to KYOTO
Morning
Must leave very early in morning i.e. 7am or so - very busy day
Arashiyama area
-Train to Saga-Arashiyama Station and hire bike
-Ride to monkey park over Togetsukyo Bridge
-wander down to bamboo grove
-walk up Saga-Toriimoto preserved street and get lunch
Train back to kyoto
Afternoon
Fushimi Inari Taisha - "thousand gates temple"
Probably 2 hours or so here - not intending to walk all the way to the top of the mountain
Night
Gion district at night for dinner
- if possible get kaisaki - looking at going to a restaurant called Yoshina - price 5-6k yen per person

Day 6 Osaka
Final full day in osaka - essentially free day to do anything left over in osaka or kyoto.
Could also use this day to travel to Hiroshima.

Day 1 Tokyo
Check out Osaka - Train to Tokyo - Check into accommodation
Explore Ginza Area (Shopping district - close center of street on Weekends)
Dinner in Yurakucho area (�eGado-Shita�f or below the girder http://www.japan-guide.com/e/e3072.html

Day 2 Tokyo
Morning
Sumo - have tickets at Ryogoku kokugikkam for the September festival
Sumo starts at 8am but probably ok to arrive 10/11am - and finishes at 6pm
Leave once to get lunch.
Night
Explore Shibuya district
-major shopping district
-large crossing area

Day 3 Tokyo
Morning
Tsukiji fish markets for breakfast
Nihonbashi district -
Akihabara
Afternoon
Harajuku area
-takeshita street
-Omotesando

Day 4 Tokyo
Visit Senso-ji temple - wander down Nakamise street and wander around the asakusa area
Travel to Shinjuku area - for afternoon
-Tokyo metropolitan building - lookout
Kabukicho region - Dinner in Golden Gai

Day 5 Tokyo
Possibly day trip to mount takao for hike

Day 6 Tokyo
At this stage not planned

Day 7 Tokyo
Early morning flight home

You could add checking out Tokyo Skytree on either Day 2 or Day 4 (depending on weather and how other activities go).

For Day 5 or 6, you could consider going to Kamakura (if interested); it's an easy day trip.

On the whole it looks good; I don't know much about Arashiyama area, but since you have "buffer" day, things should work out somehow. And if it is this coming Sept., I recommend booking accommodation soon.

Generally it all looks good, just a couple of notes. You say that you will arrive at the sumo 10-11, that seems very early to me. I love sumo but dont normally get there until just before the Juryo entrance at about 14:15. You could spend the time visiting the Edo-Tokyo museum which I liked or if the weather is nice you could visit the Sky Tree which isnt far away. As @AK says Kamakura is definitely worth the visit on one of your later unplanned days. I also agree that you need to book accommodation as soon as possible!