allocating vectors (or vectors of vectors) dynamically

Dynamically allocating arrays is required when your dimensions are given at runtime, as you've discovered.

However, std::vector is already a wrapper around this process, so dynamically allocating vectors is like a double positive. It's redundant.

Just write (C++98):

#include <vector>

typedef std::vector< std::vector<double> > matrix;
matrix name(sizeX, std::vector<double>(sizeY));

or (C++11 and later):

#include <vector>

using matrix = std::vector<std::vector<double>>;
matrix name(sizeX, std::vector<double>(sizeY));

You're conflating two issues, dynamic allocation and resizable containers. You don't need to worry about dynamic allocation, since your container does that for you already, so just say it like this:

matrix name(sizeX, std::vector<double>(sizeY));

This will make name an object with automatic storage duration, and you can access its members via name[i][j].