Optimal meeting point
There are two kinds of minimizing in this sense,


the first is to minimize the sum of the distances. 
the second is to minimize the maximum distance (finding a restaurant where the farthest friend is as near as possible).


In both cases it's not NP-Hard, since you can calculate all-pairs shortest path in $O\left(N^2\log\left( E+N \right)\right)$, sum up the distances from each restaurants to all friends and compare the sums.

Ps A special case is points laying on a line segment. The solution to the first type will be the restaurant dividing the vertices in two most-possible equal groups (has so many friends on its left as many friends on its right), the reason this works can be derived from the fact that median minimize absolute deviation.
The solution to the second problem is trivially the nearest restaurant to the middle point between the two farthest friends.

Ps2 In trees you can solve the second type using two DFSes to find the two farthest points and then choose the point in between them minimizing the distance to both of them.
The second type however, can be done in trees using a bfs traversal from leaves, counting the number of friends and distance to them in subtree of each node. Then a second bfs from the root of the tree summing all the numbers up.