Nepal has recently been in the news due to the abdication of the King, general elections, and a new government. The Maoists have joined into political dialogue and have renounced the violence that has disrupted life in Nepal for over 10 years.
Currently the Kathmandu Valley is relatively normal and probably safer than some large cities within the US. Sporadic violence has taken place, though, in the more remote areas of eastern and western Nepal. The US State Department has issued a travel warning encouraging US citizens to acknowledge concern about the potential of lingering security problems, especially in the areas formerly held by the Maoists. Warnings have also been issued for nearly 30 other countries in response to various conditions.
Travel to Kathmandu and Scheer Memorial Hospital is currently safe. The situation, though, will be carefully monitored.
To view the State Department's warning
A good site for general information about travel safety can also be found at the State Department's website.