I agree with you entirely re keeping him at home - familiarity is far more important to your old cat. Personally I'd rather have had a familiar neighbour popping in twice a day, rather than a stranger, but she won't be a stranger by the end of the week!
Paying her? - hmm, what are the arrangements you've made with her re food etc while she's staying at yours - are you leaving a fully stocked fridge for her to use - using your bed etc?
If the lads next door feed my cats when we're away, I usually give them twenty quid. If my dear friend next door feeds them, I don't pay her anything, but I bring her back a really nice gift from the holiday, and/or a good bottle of local wine. However - you really need to discuss this with your sitter, she may not be expecting anything at all - in which case perhaps you can return the favour in some other way?