Will you be pumping exclusively because you'll be away from your baby? (i'm going to assume so since it sounds like that)
If so, definitely try to pump whenever the baby usually nurses to keep your production at the same level and not change the composition of the milk.
You made a GREAT choice in pumps - the Avent has shown to be *more* effective (yields more milk in a shorter amount of time) than the hospital quality medela pumps and pump in style!! I used the Avent with my last two and it is wonderful. The only tricky part is getting the milk to let down away from baby.

Especially if you are in a crowded place, it might be a little harder than at home.
If your supply diminishes, you can always rebuild it with fenugreek (or Mother's Milk tea) and with frequent nursings at home...but I'm sure you know that
So - as for the "where" - I think the nursing rooms down there are not private, so I'd skip that...although, the mothers would certainly be supportive if you think you can pump discreetly (at least you'd have the moral support of like-minded individuals...and now that I say that - it may be easier to get letdown to happen if there are fussing/nursing babies nearby)
If it were me - and there was no way I could bring the babe - I'd pump first thing in the morning as much as I could...maybe go back to the resort for lunch and another pump in privacy...and then again in the evening either at dinner time or at parks' close depending on how late you'll be out. (and before bed) Then, be sure you pack the pumping components and freezer packs for milk storage (like the kind the formula companies give out for free - or the Avent breastmilk storage kit backpack thing). You never know when you'll have spontaneous letdown in the parks.
Then again - a lot of this depends on the age of your baby and how often they nurse. If the baby is a newborn, clearly you'll need more than 4 pumping sessions a day before you're leaking like a sieve. But, if the baby is at least, say 4 months...4 a day would be adequate...if the baby is older you might get away with pumping at the beginning of the day and mid-afternoon.
Good for you, mama!!!!