I'll third MMM's advice.
Be aware that with a JR pass, the fastest Shinkansen (Nozomi) is not covered by the pass. If you want to shave about 50 mins off your journey you can pay extra, but it's not worth it.
The next fastest service, Hikari, is covered by the JR pass, and is only slower because it makes a few additional stops. Reserved seats are included in the JR Pass (but you have to ask for them if you want them, otherwise you get unreserved), but Green Car (i.e. first class) are not, and would require an extra payment (in the region of 4,500 yen) if you wanted them. I find regular seating more than adequate on the Shinkansen, and have never bothered with green car.
I would reccommend going from Tokyo to Osaka, then doing Kyoto, Nara, etc as day trips from Osaka. Even if you visit Kyoto twice, the JR pass covers it, and it's just a short hop from Osaka to Kyoto on the Shinkansen. Osaka has the other benefit that Shin-Osaka is the end of the line from Tokyo, and getting on the Shinkansen at either end (i.e. before passengers at non-terminus stations) means you'll find it a lot easier to bag an unreserved seat. This is more important if you're travelling with others, but I've seen the unreserved cars so full that mid-route boarders have spent two hours standing outside the toilets.
The JR pass is for 7 days, and you MUST buy it before entering Japan. Once there you take your proof of purchase to one of the JR offices in a major station (Tokyo, Ueno, etc) or to the desk at Narita airport and exchange it for your pass. There is a form to fill out, and the whole process can take up to an hour if they're busy, so be prepared to allocate some time for it. Don't collect it until you're ready to use it, otherwise you'll activate it early and waste days
Your friend is advising light clothes because it will be warm, not because it will be chilly. Take a waterproof coat, though, as Tokyo's weather tends to be quite changeable on the run-up to Summer.
Whether you visit Kyoto or Nara depends on what interests you personally. I've been to Kyoto twice, but won't be going to Nara until next year, so can't really advise you there. Kyoto has one of the BEST gardens I have ever visited (the grounds of Ginkakuji), but Nara has free-roaming deer for which you can buy deer biscuits (shika sembei) and hand-feed them. Kyoto has perennial tourist favourite Golden Pavillion (Kinkakuji), the other BEST garden I have ever visited (Ryoanji), the tallest wooden structure in Japan (Toji's pagoda), and a temple with 1,001 statues of Kannon, all with different facial expressions, clothing, tools, and poses (Sanjusangendo). Nara has the world's largest wooden building (Daibutsuden Hall at Todaiji), Japan's most celebrated shrine (Kasuga Taisha), the world's oldest wooden buildings (Horyuji), and a nicely preserved area of traditional warehouses and homes (Naramachi). Obviously both cities have far more than just what I've mentioned above, but those are the main draws for tourists (well, and the Geiko district of Gion in Kyoto, but the Geiko are far harder to find than guidebooks would have you believe, and are always en route to work if you see them).
Finally, yes. Get your Yen before you go. Not only is getting it done there a waste of your time, but you get to watch the rates for a little while and buy when it's at its best. You don't have much time to do this in, so you might just have to bite the bullet and get the rate as it currently stands, but it's something to think about next time you want to plan international travel. The dollar is a little weak against the yen at the moment, but it's not a deal-breaker
I'm sure you'll have a great time. Japan's a fantastic place to visit. Take a little time to learn some basic Japanese and customs before you go (I always learn at least yes, no, please and thank you in a destination language before travelling, but if you have specific medical needs, DO take time to learn appropriate phrases, e.g. "I have asthma", "I am allergic to aspirin"). Be sure to get the basics right, which I'm sure your Tokyo relatives will help you with if you ask them - what side to use the escalator in Tokyo vs. Osaka, what noises not to make at the dinner table, what not to do with your chopsticks, etc.
Don't expect Japan to be perfect. It's certainly safer than just about anywhere else in the world, but hanging around in the arse end of Shinjuku at 3am getting roaringly drunk in seedy bars is just as foolish as walking down the street in broad daylight in Compton, LA
