Is the JR pass worth the expense?

We're planning a 14 day visit. Roughly half of it in Tokyo and half in Kyoto.

We still have to decide on the flight. We might land in Tokyo and leave from Osaka, so that would make the JR pass not worth it, but should we decide to land and leave from the same airport (or city anyway) we would have to get a return ticket for the shinkansen. Would it be worth it then, considering we will be using public transport in both cities?

I know not all public transport is JR, I'm not sure how to evaluate how much of the JR public transport we'd be using and whether that would make the JR pass worth its price.

Yes.

Buy a one way ticket either from Tokyo to Kyoto or vice versa (nearest Airport to Kyoto is Kansai international Airport). Get a Suica from JR East in Tokyo or ICOCA at Kyoto…

JR+Shinkansen pass gets you to any city in Japan.

My suggestion would be to grab the Lonely Planet Guide to Japan As soon as possible.

A seasoned traveler, would create an itinerary based on a 7 day pass. For example, if you were to go to Osaka, you would stay there 3 days and explore Kyoto, Nara and Osaka without activating the pass. To get to Miyajima, Hiroshima, Iga, etc. That are a little farther away (including a hot spring resort that I've forgotten the name where everyone walks around in robes visiting 7 different spas), use that pass so that you can still use Nara or Kyoto as a base and then head to Tokyo where you may want to visit Mt. Fuji, Nagano, Hakone or just use the JR system to get around the city (which is far more extensive in Tokyo than Kansai). A shinkansen ticket is usually around $100+ one way so a day trip from Kyoto to Miyajima or Hiroshima pays for the passes already.

The way to evaluate is assume you are making a day trip from let's say Kyoto to Nara -- you can walk most of the city and sites so your only cost would be round trip tickets from Kyoto to Nara station via Kintetsu or JR ($8?). Unless you are spending $30 per day per person riding local JR trains or plan to use the Shinkansen 9 of 14 days, you won't get your money's worth from a 14 day pass.

BUT There's definitely something to be said for having the luxury of travelling anywhere you want, whenever you want, as often as you want without having to worry about always having to buy tickets for the entire vacation -- especially if you are a MUST SEE IT ALL type of traveler. This is kind of a once in a lifetime thing so this kind of freedom to some is worth the extra $150-$200. For example, what if someone in your group gets sick in the middle of the pass activation or there's a festival you MUST go to in Nagano on the 1st Day of the trip…

Create your itinerary and then decide… And don't forget that Lonely Planet Guide.

[EDIT: I forgot to mention, these JR + Shinkansen passes are only available outside of Japan and are usually purchased from a travel agency -- look for one specializing in Japan travel)]

If you are going open-jaw, it could very well not be worth it. This is especially true if you are going to use ANA's special deal for foreign tourists to get from Tokyo to Osaka. In Tokyo, Kyoto and Osaka you are probably going to be on the metro or private lines sometimes where your JR Pass is not valid. For example, the SkyTree station is Oshiage-which is not JR.

If you are only going to stay in Tokyo and Osaka, then the JR Pass is not worth it. The JR Pass saves you money only if you plan to travel extensively over distances (such as between cities). For within a city, you are better off using the other passes or pay as you go.

JR Pass is worth if you take a long distance train many times during the validity period. According to your story, you would just go from Tokyo to Osaka and back. Not sure if the 14-day pass is worth in your case.

I'll give you the best solution, the one nobody else will ever give you (or even bother to learn about).
Flying single open jaw would be the best option, but you already know that. First though, you must decide your itinerary. You are going to Japan to see Japan, not in order to make a rail pass pay off. So once you have your plans, you will be able to decide definitively what transport method is the best.

Many people as first timers to Japan spend half their time in Tokyo, and the other half in Kansai. Nothing wrong in that; there are numerous good sights. But you should decide according to your own interests - and only you know that. If you spent 7 days traveling from Tokyo to Kyoto and back, the truth is that you'd still fall a bit short from making a 7 day rail pass pay off (though one trip on the Narita Express would make you break even). And if you got a 14 day pass, you'd be losing about

If going to Kyoto and back within 7 days, the most efficient and time saving way would be the japanican ticket.
http://www.japanican.com/en/tour/detail/VJOPENTK1/
You can use the fastest bullet train (Nozomi) and get there in about hours. It is way cheaper than the 7 day JR Pass, and it even includes one day of local transport. It does not cover travel between the Kansai cities, but they don't amount to that much and you still end up ahead.Speaking of which, in addition to Kyoto, you should definitely make some time to see Nara as well.

But if you plan to expand your travel, like a day or overnight for Hiroshima/Miyajima, then the JR Pass is the way to go.

For within Tokyo, one of the best money saving ways to get around is the 2-3 day subway pass.
http://www.tokyometro.jp/en/ticket/value/travel/index.html#anc03
And the Tokyo area, there are many good day trip possibilities too. A Tokyo Wide Pass can save a lot.
www.japan-guide.com/e/e2361_06.html
For some other good tips, try:
http://www.thejapanfaq.com/the-best-japan-travel-tips/

Be sure to do your research - look at the official city websites for some good sightseeing guides, plus jnto.go.jp and japan-guide.com
http://www.gotokyo.org/en/index.html
http://www.pref.kyoto.jp/visitkyoto/en/
http://www.kyoto.travel/
www.japan-guide.com/e/e2165.html