Macapá is the capital of Amapá, and arguably the most deserted state capital of Brazil. As it sits north of the immensely wide mouth of the Amazon river, there are no highways leading out. Unless you count the road into French Guyana, that is.
Most mid-scale hotels give a straight 20-30% discount on posted prices.
Perhaps the only internet option on Sundays is inside the Mara Hotel at Rua São José just off the corner of Rua.