You'd have to visit the LVA office (during business hours, of course). It's not all that close to downtown--near the corner of Valley View and Twain, about a mile west of the Strip.
If the timing's right, maybe you could stop by LVA on your way from the airport to wherever you're staying downtown. It wouldn't be that much of a detour. So if you're taking a cab to your hotel and you can get there before 5 pm, great. Obviously, if you have a rental car, you're good.
There really isn't a good transit option (there are frequent buses up and down Valley View, but...yuck) and it's not within easy walking distance of the Strip.
It will be worth a little trouble and expense to pick up the book, especially since you'll be downtown--you can recoup your membership fee and then some just by redeeming all the downtown coupons. I believe there's over $100 worth you can use within a few-blocks area.
(Also a possibility: take the Strip bus (the Deuce) to Twain and LV Blvd and cab over to LVA and back.)