I have lived in Japan for two years, and had stayed at a temple several times before (for work, actually) ... in others words, I'm used to the whole "temples & shrines" side of Japan, and it takes quite a bit for a place to impress me. Mt. Koya itself is a 5 star experience ... where to begin? The Oku-no-in cemetery lives up to its reputation and then some (especially at night!), Kongobuji's sliding screens are quite beautiful, and the Garan complex is impressive as well. I definitely recommend doing the Jukai ceremony as well (at Daishi Kyokai). The whole ambiance of Mt. Koya is simply sublime and indescribable. Thinking about it makes me want to go back!
Ekoin itself, I would give 4.5 stars if I could ... I went back and forth between 4 and 5. I really like the place, but I try to reserve "5 star" recommendations to the places I couldn't really imagine NOT going back to should I go back. Ekoin would definitely be on my short list, but I can't say I wouldn't look into someplace else too that grabbed me.
The place is run by a bunch of friendly young monks who run around in sweatpants and t-shirts most of the time (making their "transformation" into the formal Buddhist robes for ceremonies particularly striking!). The ceremonies really are a highlight of the place, particularly the fire ceremony. Particularly if you are new to Japan, I imagine the whole experience would be rather out-of-this world, and even for travelers experienced with Japan, the ability to get a glimpse into (and participate oneself) in this esoteric lifestyle is still very special. The food is quite good, and quite healthy (vegetarian). The rooms are spacious, and while not as luxurious in the way a ryokan might be, still as nice or nicer than your average minshuku ... after all, this is a temple ... what luxuries I found were a pleasant surprise (the place I had stayed at before was nice but more austere).
It's right by a bus stop and is easy walking distance of Oku-no-in, although the Garan is a bit of a walk (but still quite walkable). The price is reasonable (I paid Y10000/night as a solo traveler, which seems to be the going rate) ... whether that is cheap or pricey depends a bit on your reference point (a fancy ryokan in Kyoto would go for several times that; a budget hotel in a medium sized city would be a fraction of that). Like most traditional Japanese places, prices are per person rather than per room (nice for solo travelers).
No real glaring negatives. When I reserved the room, I'd asked to take part in meditation and sutra copying, but that never materialized so I was a little disappointed (I could've asked, but as I said, I'd stayed at temples before so I had done these things). Note that although the curfew isn't until later (I forget when exactly ... I assume there's a curfew, but now that I think about it I'm not sure; "night life" in Mt. Koya is a trip to the cemetery, not the bar!), the main gate is locked earlier (just go around the side, around where they do the fire ceremony). The bathing area was ok, but nothing to write home about. The walls are relatively thin; I had somewhat noisy neighbors one night, but fortunately they didn't stay up too late. The futon's a bit hard. The monks were friendly, but a little distant (and always seemingly quite busy) ... it would've been nice for a chance at a little more interaction and conversation. No door locks, which made me slightly nervous about leaving stuff in the rooms (my concern was not the monks, of course, but fellow tourists). No major issues, but enough to keep it from being a "five star" experience.
Basically, if you are going to Mt. Koya, definitely stay in a temple lodging. I really liked Ekoin, and my criticisms are all pretty nit-picky. There are some places I've stayed at around the world where I'd go back in a heartbeat. Ekoin's not quite in that class, but I'd certainly enjoy a chance to go back if the opportunity presented itself.
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC