I've been going to the Goodyear Auto Service Center on North Glebe Road in Arlington for more than 10 years. This store is a cut above the other locations in the area because it is a corporately owned store and not a franchise. They are not the cheapest but, they do timely, quality work. It's also located across the street from Ballston Mall so, you can go ice skating, watch the Caps practice, shop and or dine while you are waiting on your car.
I would avoid BJ's Wholesale Club for tires at all costs. Yes, they have great prices but they only stock crappy tires. If you require a mid-grade or performance or above quality tire, they have to order it, your order has to be paid in full prior to ordering and it takes a week or more. They keep their prices down by limiting their in-stock selection.
They also do not employ people with the same skill level as Goodyear. And if all of that wasn't enough, since most tires have to be ordered they will repeatedly try to upsell you into more tire than you need. When I price shopped them, they attempted to sell me a performance tire, when I requested an all-season tire because I drive up North a lot in the winter. I immediately left at went to Goodyear.
Regardless of where you buy tires, KNOW what kind of tire your vehicle needs and what type of tire you want to put on it BEFORE you purchase the tires. There are many good online resources for this. That way when you walk in you can say, "I'd like to buy (brand) (model) tires for my car. Do you have those and what's your price?" A good salesman will still try to upsell you to something else, but do your homework and stick to what you need. If they keep pressing, walk out.
The WORST thing you can do when buying tires is walk in and say, "I need tires. What kind do you recommend for my car?"