Hospital Fees

In actual truth, both of what you have heard are true.
- if you go to hospitals where all the westerners are likely to go, seeing a doctor there is likely to set you back a pretty penny. When I say that, I am thinking in particular of places like Norvic International Hospital, CIWEC and perhaps one or two others, which cater to the well-off in the international community.
- if on the other hand, you go to TU Teaching Hospital, for example, where many nepali people go, you will only only be asked to pay a nominal fee of 50 rupees (only) to enter and very reasonable additional amounts for care on top.
No comparison, really, between the two of them in terms of costs. The first type is expensive by any standard, and the second type, I always found to be, very affordable for my pocketbook.
But does that mean that the first type is superior the second? The answer is definitely NO and the reason is that in Nepal, it is not uncommon for a selected number of good reputable and most competent nepali doctors to work in both types of institutions.
Therefore, if you can determine that the specialist/doctor you want or need to see does indeed work in both institutions, on selected days - don't hesitate, head to TU or similar and consult with him there - In terms of obtaining good personal medical care it's best and cheaper that second way too.
I looked into Cigna fees at one time. I found them to be very high and renounced for that reason.
As for the budget you mention, a quick calculation shows me that your figure falls within the parameters of the "low and high" bracket given by this other contributor on these pages not so long ago.

Bienfrancaise, so true. I've found the trick to be that if there is an INGO attached you get just about that same level of care as in that country.

I live over in the Bhaktapur area, so I like the Kathmandu Teaching Hospital in Dhulikel. My blog is listed on this site and I've got a few posts about healthcare in Nepal.

Let me be clear on the following. It seems to me that the starting point in any search to find the best doctor in town is for the person to decide - first and foremost - what kind of medical care you require? Where to get that medical attention comes second, in the order of priorities. First, are you looking for:
- a cardiologist, or
- a dermatologist, or
- a gastroenterologist
- an ophtalmologist
- a neurologist
- an osteopath
- or a gynecologist? or some other specialist, in strong preference - to consulting with just any "GP" (a general practitioner). There is a multitude of reasons for my putting it this way. But suffice it to point out that if you see a Specialist, you are much more likely to be consulting with a very Senior Doctor, a distinct advantage in my view. 
I would therefore recommend that you do some asking around in Kathmandu after you arrival here in an effort to determine who's number one with the best reputation in any one specialty field. After you've asked around and gleaned hopefully good and reliable advice from friends or those around you, you can proceed and head to TU Teaching Hospital or some other well known clinic where they don't charge an arm and a leg, like I said before, in a concerted effort to consult with him/her there.
It is much better to go to the nepali hospital - with a name - after you'e determined what particular doctor/specialist you want to book an appointment with. Going to the same hospital "blind" - without a doctor's name - might be a mistake and is what, I personally, would avoid to do. 
That's my view anyway.

Thank you very much, really helpful!!

As far as the budget goes, what does "low and high" mean? I have tried to find it in the forums but I can't seem to find it.

Check out "Housing Location & Lifestyle Question" where in replying to AlisonDK on 16th September last, our fellow contributor expressed the view that "...you can live pretty well on $1,500 - $2,000 a month..." All I was saying is that the budget figure you cited just fell within those parameters.

I quite agree that whenever possible, it's far better to consult with a specialist doctor than with a GP especially in a country like Nepal. Obviously, a specialist doctor is also more apt to have spent a greater number of years in medical schools and very possibly getting his degrees abroad than the average nepali GP counterpart. My understanding is that only about 1/3 of the doctors in Nepal ever get that golden opportunity to study abroad.
It's also more likely that the best and most experienced of those specialist-physicians will have chosen to be exercise their profession within the greater Kathmandu area, in preference to out of city. The top ones will be working in hospitals like TU Teaching Hospital, and the like, within city limits. So step one is to seek out the top name in any given medical specialty, then to find out which hospital that specialist exercises in, and third to book an appointment to see him/her, within the complex of the given nepali hospital.
If the specialist you've chosen happens to work part-time in both a nepali and international hospital/clinic in Ktm, be sure to consult with him within the nepali hospital context. You'll get identical care and attention from said specialist, but at a fraction of the cost.

The high end is CEWIC and such that take traveler's insurance. The doctor visit will cost around $80. As one of the commenters said, these doctors practice in other hospitals.
I got pneumonia one time and I went to an excellent hospital (with a Japanese presence) and the entire thing including a pulmonary doctor in the middle of the night and a cardiologist was maybe all of $50. The did the entire scope of tests including black mold and they treated me better than I'd ever been treated at a hospital. Here are a few prices from places I found and got good service at:
Dental MRI:  $11
Teeth cleaning at a very clean and modern teaching hospital: $4
Root Canal at a private dental clinic that included another tooth, as well.  $230
I paid for a Nepali to have eye surgery, not sure if it was cataracts or glaucoma, but it was $110 per eye for the computer/laser equipment. The doctor is world renown for eye surgery and he's just right here in the Kathmandu Valley.
You need to know where to go, like another commenter here suggested, but you can get excellent healthcare. I wouldn't suggest open heart or brain surgery, but there are many possibilities for some great bargains. It's only a great bargain if all goes well, so do your research and be careful about infection.

Glaucoma and cataracts are two very different things. Glaucoma is an eye disease which is associated with elevated intraocular (IOP) pressure in which damage to the optic nerve can lead to loss of vision and even blindness. Glaucoma is in fact the leading cause of irreversible blindness in the world.
Glaucoma cannot be cured but it can be controlled.
An authority on the subject will know.