How about grabbing a bite tomorrow?

Literal

Tomorrow, meal [for-example-でも] how?

でも after a noun means 'or something like X' — a casual, non-committal way to suggest. 食事でもどう? = 'how about a meal, or something like that?' The non-specificity is socially lubricating, leaving room for the listener to counter-propose. Textbook-perfect casual invitation.