Get a snack going through Dallas and Wichita (8)

I believe the answer is:

sandwich

I'm a little stuck... Click here to teach me more about this clue!

'get a snack going' is the definition.
I can't tell whether this defines the answer.

'through dallas and wichita' is the wordplay.
'through' says the answer is hidden in the clue.
'SANDWICH' is hidden in the letters of 'dallas and wichita'.

Can you help me to learn more?

(Other definitions for sandwich that I've seen before include "Maybe double-decker" , "Snack; sponge cake" , "Resort" , "Pieces of bread with filling" , "One of the Cinque Ports" .)

I've seen this clue in The Globe and Mail.

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