I have been to Nepal without a visa. - Our plane destined for Delhi, India had a problem and we set down quickly at Kathmandu. We spent 4 hours under the wing in lawn chairs waiting for parts and a repair. The airport the does accept some limited international flights and can handle a 330 Airbus if necessary.
There is a site (http://www.nepalembassyusa.org/visa.php
) that gives information on obtaining a visa if you have a U.S. passport that will not expire until more than 6 months after arrival. It can be obtained by mail with a check (not personal obviously). The site provides visa information.
An alternate is to Google Nepal visa to get other information.
The government has undergone some changes is the last few years after becoming a Republic, so get current information rather than relying on experiences. I think there is an office in NY somewhere.
Not all of Nepal is like Kathmandu, which is a large city and local transportation beyond there is highly variable, slow and unpredictable.