There are several city guidebooks for Kyoto. You obviously need to buy one, along with maps of both Tokyo and Kyoto. Go to the Travel section of the nearest large bookstore.

You don't need to take a cab to get to the commercial center of Kyoto. The subway will take you there for much less. Even so, there's a lot to see within walking distance of the station.

If your budget is $200, you have a huge choice of hotels in both Tokyo and Kyoto. Choose a few on the basis of their proximity to what you want to see, and then go to their websites to see what they offer. You have to go way down in price to the backpacker hostel level before you have to worry about cleanliness or safety. Non-smoking rooms are pretty common these days, but large rooms come with a high price tag. No problem though, because with such a short time in each city, you're not going to spend much time in your room.

Any hotel in the $200 range will hold your bags for a couple of days.