I would use the butler for restaurant reservations, especially for in house restaurants, but probably not for suggestions. A butler is not a concierge.

Wake up call requests
Request to restock minibar
Morning coffee delivery
Request to call taxi
Requests for bell persons
Laundry and dry cleaning pick up and delivery

Many requests that you would otherwise make through a hotel "service express' (or whatever the property calls its all purpose service phone line) you can also do by contacting your butler. Your butler can function as an assistant who then arranges hotel services with the approriate department within the hotel at your convenience, rather than you figuring out whether to contact housekeeping or the concierge for an electrcal outlet adaptor, housekeeping or room service for ice or a bottle opener, etc. The butler also does a lot of fetch and deliver type errands, so getting a bunch of photocopies from the business center would also work or a simple request from the hotel's giftshop. The butler can schedule housekeeping times for your room and get additional toiletries for you, or robes and slippers if they're not in the room.

You could also think of the butler as a more personal mini version of whatever/whenever.

There's so much confusion that it's almost a shame that the hotel services book doesn't have more detailed information on what butlers can do or alternatively that there isn't a letter in the room upon arrival introducing your main butler and describing the services, perhaps with a note about the butler's qualifications (languages, local interests/expertise (sports, food, museums), previous hospitality industry experience, etc.).