Just to add to all the excellent previous advice: it used to be the case that you could only buy a Japan Rail Pass from outside Japan, so this had to be organised before you go. It's quite easy to do, from a travel agency. You get vouchers which you then take to a JR mainline station once there, to exchange for the pass. I haven't been to Japan for a few years, sadly, but Wikipedia claims they're currently running a trial of selling the passes in Japan, but at a higher price, so probably still best to buy them here.
They may not seem cheap on the face of it but will save you a very significant amount if you travel by train, especially by shinkansen (bullet trains).
As for getting around - all Tokyo trains/subways have English announcements. Lots of people, especially younger ones, do speak English, as they learn it at school, but are shy of using it in public; however, people are wonderfully helpful. We had no trouble getting around and we went all over the place.
You can find cuisine from all over the world - Italian is hugely popular, I guess because of pasta being so similar to noodles, but also French patisserie, and there are Irish pubs, etc etc - but you can't beat proper, cheap and cheerful ramen, sold at a million tiny places everywhere. Eating out can be hugely expensive at high-end places, but cost very little if you eat where the locals do. We always end up bringing money back. Alcohol in fancy bars is ££££ ( or rather ¥¥¥¥) but a few beers in eg a neighbourhood Lion Beer Hall won't break the bank.
You could easily spend a month (or longer) in Tokyo, making trips out, but a week or so in Kyōto (with trips from there) would also be a good idea. It's much more spread-out than Tokyo and travelling between temples takes much longer. Personally I prefer Tokyo but that's just me....it seems livelier and buzzier and although I love visiting temples, I do get a bit templed-out after a while.
If you look for hotels in Tokyo near the big stations, you'll save time when you want to make trips out. So as a pp said, places like Shibuya, Shinjuku, Ueno. Shinjuku is a massive station with numerous large hotels in the vicinity. The challenge then is to master the geography of the station, which is virtually the size of a small town 
If you go any time from late September onwards, you can be edging into typhoon season, when it's still likely to be very warm and humid, but also rainy and (extremely) windy. We had a bit of a nail-biting experience once, complete with cancelled shinkansen and being stranded miles from our base, due to a typhoon, so it's something to bear in mind when choosing the time to go.
BUT having said the above, it's a wonderful, fascinating country and I can't wait to go back.
Sorry for epic post. As you can tell, I'm bit obsessed 