The Serbian to U.S. exchange rate is fantastic: $1 equals about 105 Serbian dinars, which goes pretty far in this affordable country. Budget hotels can cost as low as $20 per night, and you can eat a good, cheap meal for about $5 and add a beer to that meal for less than $2.
If you stay in Belgrade, there are plenty of free attractions like the Belgrade Fortress, St. Sava, or Ada Lake. Rent a car for less than $35 per day, and you'll be able to easily see a lot of the Serbian countryside which includes monasteries, national parks, vineyards and charming towns all at a low price. The only thing you might be concerned about is the cost of a summer flight which ranges from $750 to $1,000.