According to Scott's paper "The geometries of 3-manifolds", the only closed manifolds that admit an $S^2\times R$ geometry are the two $S^2$ bundles over $S^1$, $P^2\times S^1$ and the connect sum of two copies of $P^3$. It seems like the last one is the only candidate (unless I'm missing a way in which $S^2\times S^1$ can be viewed as such a bundle).
(How do I get a connect sum symbol in maths mode!?)