How’s my itinerary? JR pass make sense?

I visited Japan about 3 years ago with a couple friends, and spent over 3 weeks there. During that visit we stayed in Sapporo, Tokyo, Osaka, Hiroshima, Fukuoka (Sumo Tournament), and Kyoto. We did tons of day trips, including Yokohama, Kobe, Nara, and Miyajima. Now I'm planning a trip with my fiance and my brother, neither of them have been to Japan before. This time around, we will only be there for 14 nights for pleasure (I'll be in Tokyo beforehand for work). We all agreed that we're not going to go crazy, so ideally it will be a bit more "relaxed" pace and avoid rushing from train to train every day, hotel to hotel, etc. Having said that, here's my current itinerary:

day 1 - Hakone (from Tokyo) : we'd leave early AM and arrive in Hakone for lunch. Spend the night at a ryokan. Is this worth doing? Last time I didn't visit any hot springs, and Hakone seems to be a nice (but expensive) place to splurge for a night and have the experience?

day 2,3,4,5 - Kyoto (from Hakone) - 4 nights in Kyoto. We are planning to do tons of day-trips (fushimi inari shrine, Nara, Kobe, Himeji, ...)

day 6,7 - Osaka (from Kyoto) - 2 night - We're planning to go to fuji-q for a day, but I'd also love to have at least one late night at Dōtonbori. Here's my first dilemma: I realize Kyoto and Osaka are ~30min bullet-train ride from each other, so we're effectively spending 6 nights in that area. Would I be better off staying in one place (Osaka, or Kyoto) as a central hub? I'm sure we will want to partake in then nightlife multiple evenings... so would 4 nights in Osaka and 2 in Kyoto make more sense?

Day 8 - Koyasan (from Osaka) - overnight in a temple

Day 9 - Hiroshima (from Koyosan) : I know some people just do a day trip from Osaka and are able to visit both downtown Horishima and Miyajima in a single day-trip but that seems too rushed for me. Now, I've been to Hiroshima before and already seen a lot of the downtown, as well as Miyajima, but I didn't want to rob them of those experiences.

Day 10,11,12,13,14 - Tokyo : planning to again do lots of day-trips, but also just explore as much of Tokyo as possible

So, how does the above itinerary look in general? What would (or wouldn't) you change? Originally the plan was to also include Takayama, Kanazawa, and maybe even Shirakawa-go, but it looked like that was getting away from the "relaxed" pace we're going for (was thinking only 1 night in each of those places, so lots of moving from ryokan to ryokan, catching trains every morning, etc). Was it a mistake to cut those? Should I have cut out Hiroshima, and maybe free up a day or two from Osaka,Kyoto,Tokyo to visit them?

I'm also not confident that the 14-day JR-pass would be best "bang for buck", but we will be doing tons of "day trips" from each of the different places. I know there are other passes to consider as well (ie. Kansai Thru-Pass, or even pay as you go), but given I'd like this to be more "relaxed" pace, I'm tempted to just go for whatever is most convening/less hassle to facilitate. Appreciate all comments/feedback/recommendations :-)

Like you said yourself, You will do lots of daytrips, and only use the JR pass few times. Plus within Tokyo, Osaka nor Kyoto you wont be using the JR pass that often. I suggest you to just buy each ticket individually. Or if you don't mind taking a bus for a long journey, then take a bus, it's even cheaper than bullet train.

Kyoto and Osaka are not 30 minutes apart by bullet train; they are 30 minutes apart by Special Rapid Service train. The shinkansen takes about half that time. Many people do just stay in one of the two cities and day trip to the other.

I'd take one day out of Tokyo to be able to spend a whole day at Miyajima. As you said, you don't want to rob your companions of the experience!

You can work out if a rail pass will pay off yourself. Use Hyperdia (hyperdia.com/en) to look up the fares, add them together yourself and then compare the total cost to the cost of a pass. Or, use this calculator: http://www.aoimirai.net/japan/jrpass_calculator.html

I think a 14 day pass would work if you are happy to use trains.

Tokyo to Osaka is 14,XXX. Osaka to Hiroshima is 10,XXX. Train and ferry to Miyajima is 590. You need to double these amounts for return fares.

Just the shinkansen trips along equal 48,XXX yen. That is more than the cost of the 46,XXX yen 14 day pass.

Add in day trips like Miyajima, Kamakura etc (1200-1800 yen per day) and you go well towards 60,000 yen, if not above.

Thanks for the responses! After spending more time thinking about Hakone (and the price of staying there), I've revised my itinerary a bit. I'm now leaning towards cutting Hakone, and spending one less day in Kyoto/Osaka, and then heading to both Takayama and Kanazawa - 1 night in both places. I realize I said we were going for a "relaxed" pace, and the long train ride and short stay in those two places certainly isn't "relaxed", but they both seem so unique from the rest of the trip, I've never been to either myself, and I'm hearing that the train ride to Takayama is beautiful. We will shorten our stay to 5 nights in Osaka/Kyoto, and probably do 4 nights Kyoto 1 night Osaka (or vise versa). Hoping this change isn't too ambitious, and I won't regret cutting Hakone (thinking we can day trip there or Mt. Fuji from Tokyo if we really wanted anyway)?