OK...the way I would approach this is to have the three fields you suggest on the form, but to have a CONTINUOUS form. I think Access calls this a muliple item forms now in Access 2007.
So you will eventually build up a long list of records, each row having date, park and attendance number.
But instead of having to enter the same date five times (which I think is what prompted you along the lines of your screenshot), I created a new field at the top of the form, where you enter the date once. Then each time you enter a new record it picks up that date automatically.
So, on day one, you select the date, then enter as many attendance numbers as you want. Day two, come back and change that date at the top and then enter five more parks. I made the Park field a combo-box (dropdown option), based on a separate table where I entered your five options. If you ever need to add new parks to your list, just add them to that table and they'll show up in the combo-box.
When you unzip and open this, open the form in design view and you'll see where I've explained what I've done. Hopefully this will be enough to get you on your way.
Should you buy a thick Access book? Hmm... maybe! I've been where you are and I know how frustrating it is when you don't have some of the basics.
But you can learn a lot online and there is a WEALTH of experience on this forum. I learned just about everything I know (which isn't a great deal) right here and I keep coming back for more.
Let me know how you get on with this. Good luck!
Pat.