A couple of comments on your itinerary.

Yokohama, which I've visited several times for work purposes or to meet friends, is not all that different from Tokyo. I'd just go straight to Kamakura.

There's no need to change hotels in the Kyoto-Osaka area. Kyoto has quite a different ambiance from Tokyo, but you can easily see what there is of interest in Osaka in a day trip from Kyoto. (In my mind, not having to change hotels is a good thing.)

The Suica will take you on all public transit in the Tokyo-Yokohama area except for a couple of lines that you are unlikely to take (e.g. the Joso Line out of Moriya). According to the map that I just downloaded, the covered lines include the Minato Mirai line, so if you do decided to go to Yokohama, you don't need a separate ticket. The map is here:

http://www.jreast.co.jp/e/pass/suica.html

The Miyako card is good on all private rail lines in the Kansai area. You could use it to take the Kintetsu line to Nara or one of the private options to Osaka. Once you arrive in Nara, everything is within walking distance. In Kyoto, get a map of the city and arrange your sightseeing so that you see things that are close together on the same day.

The large international-style hotels may have more English speakers, but they're also really, really expensive unless you can go on points. One of the great things about Japan is that you can find clean and safe accommodations in the budget category quite easily in the so-called "business hotels." The staff may not speak much English, but if they are under the age of 70, they will have had at least three years of written English in school, so you can communicate by block printing your questions. Alternatively, there is likely to be someone on the staff who speaks better English than the other employees and is the go-to person when it comes to communicating with foreigners.

Japanese customer service tends to be excellent, and if you have a question or problem, hotel staff will do their best to work something out.

Rooms at business hotels are small but contain everything you need, including a tiny private bath that looks as if it was carved out of a single piece of plastic. Some of them include a breakfast buffet or at least coffee and rolls. Prices are US$100 per person or less.

These days, it's easy to find hotel booking sites and reviews online. (I had excellent luck finding good, reasonably priced accommodations in pricey Scandinavia this way.)