Unlike with a childminder, a nanny is your employee so you can tell them what to do.
You could certainly leave out a pre-prepared lunch, though you may prefer your son and nanny to eat together - so perhaps leave sufficient supplies for both of them to eat the same thing.
Communication is key. You need to come up with a way of communicating with your nanny on a regular basis, so whenever any information needs to be passed to the other person (so you to nanny, nanny to you) you have a system in place for doing that. Personally I quite like using Email for that, but not everyone likes that method. A note by the kettle may work just as well.
When you interviewed your nanny did you talk about what you expected them to be doing during the day? Some nannies love going out and about (I would say I'm like that) where as others love Arts & Crafts (I'm not great at that), others are good at music, lets pretend, etc. Play to your nannies strengths, so your son gets to do things which your nanny is good at and likes doing.
Sure you can say you would like him to be taken out somewhere... but where? At first you may need to give a list of suggestions of places to go, especially if the nanny isn't that local to you. Your nanny on the other hand may know of some great places to go, so may not mind at all being left to find their own places to visit.
Budget - how much money are you allocating to outings? Trips out can cost money, so perhaps allocate a budget to it so that your new nanny has some idea of what sort of things they could do, and what is out of budget (if your son wants to do something that is over budget, they could perhaps use two weeks budget on that thing, and not use any budget the prior/next week).