at indicates place/location seen from a distance to shows direction (including for moving, as in this case) In many circumstances, they are used interchangeably. You'll have to do searches on the net to see which is prevalent in a circumstance or another. At Yahoo: "take her to a restaurant" 856 hits, idiomatic because it shows moving "take her at a restaurant: 0 hits, thus not idiomatic "take her to dinner at a restaurant" 11 hits, idiomatic because shows place for diner "take her to dinner to a restaurant" 1, thus less idiomatic Also, make a search at this site with: at to (top right Search corner) to see related threads.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.