A good sense of humor is probably the most important aspect of this date. Once your companion realizes you're headed to the Dollar Store, there might be some initial resistance. For that reason, it's generally best to keep it cryptic about the destination address.
But fret naught, it's easy to overcome and I explain exactly how I conduct this outing.
Obviously, without a Dollar Store... this date pretty much doesn't work.
And of course, without your $5+, you'd otherwise be leaving empty handed.
Take your date by the hand, and walk each isle, suggesting items for one of their 5 and asking their opinion on each thing that catches your eye. At the end, ring up your purchase and go find something fun to do with the 5 items.

I almost made this mistake once and had to rush to make it with my date before they closed. So, lesson learned is check the store hours during the planning phase of this outing. 9pm was when the Dollar Stores closed for me, but Dollar Tree or Dollar Emporium or Dollar-Whatever you have in your area probably have different hours.

Better make sure there are at least a couple options in your area and you're not having to drive 45 miles each way to spend $5.