A few of the churches that have things going on for singles:
New Life Church, Sioux Falls, South Dakota - Home
Church at the Gate - Sioux Falls, South Dakota - The River
Embrace Church
Mercy Church:: A Place for Sinners! Belong, Share, Question, Grow
Of course there are lots of churches, so there's more.. just a few that came to mind.
My personal opinion (and I am single female also), I would live on the South or Southwest side of town. It just has a nice "feel" to it (safety, nice areas, within good distance to shopping, interstate).
On this website you can search by location for apartments, on the map the area I'm talking about is in the lower left side, (west and south)...
Search Results - ForRent.com
There's alot of options, but that's just a start