Mitch, it doesn't matter how many receptacles are on a circuit, only how much power is being used. The dining room receptacles should be on a 20-amp circuit, and are probably on one (or both) of the kitchen appliance circuits, which are 20-amp circuits.
Idling current of modern electronics is rather low these days, and I was running my entire setup on one circuit when we were renting this house; somehow, I didn't need to upgrade the power until we bought the house. Isn't that wierd how that happens?
In any case, I wouldn't worry about it until you try the setup. If there's an overload, you'll see it in the lights dimming to the beat of the sound. As for the cost of running a circuit, there's no way to give more than a price range without coming there.
An electrician would have to see how the new wires would run from the panel to the new location, and you'd have to decide where and how many new receptacles to install. It's possible to re-feed an existing receptacle, or just add a new one.
Larry
www.fineelectricco.com