Oh dear, this is all very distressing at the start and I found this the toughest thing. I wish now that I had just come clean to start with and explained- after all, your friend wants to see you, and probably won't be bothered if you are eating or not. I was so nervous about telling people, or sitting with them not eating- but when I did it, I was surprised to find they either didn't notice or didn't care!
If it were me, I would give your friend a heads-up about it beforehand, and if you explain that it is important to you, maybe she will change her mind and suggest you stay in, or go somewhere a little 'easier'?
Good luck either way- I do think this is the toughest thing to negotiate, but it can be done!