According to Scott's paper "[The geometries of 3-manifolds][1]", the only closed manifolds that admit an $S^2 \times \mathbb{R}$ geometry are the two $S^2$ bundles over $S^1$, $P^2 \times S^1$ and $P^3 \# P^3$.  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).

*Edit.* As pointed out below, I spoke too soon. Of course such bundles could have spherical geometry too.  Scott's paper is a nice reference for that too!

[1]: http://blms.oxfordjournals.org/content/15/5/401.short?rss=1&ssource=mfc