Not sure of your time schedule, but here's the BBQ scene closest to downtown..
Pinkerton's, Gatlin's and Killen's are the "real" BBQ joints near downtown.
Pinkerton's is the closest (4 miles). Not too much of a traffic issue. Will have normal weekday rush hour stuff starting about 3 or so but it's not terribly far so it's the least headache of them all.
Killen's is more famous, but it's in Pearland which is a suburb on the outskirts of the city. It's 22 miles, not 16. The 16 is if you take Telephone Road (35) behind Hobby Airport . That street is a war zone and I would not recommend you get on it. You will have to take 288 or I-45 down to Sam Houston Toll Road. Then take the Sam Houston Toll (stay on side feeder road along side Sam Houston Toll Road which is called Beltway 8 to avoid tolls) to 35 and drop down into Pearland to Killen's.
Summary:
If you have a lot of time early during a weekday or will be around on a weekend with half a day to kill, I'd try Killens. If you are pinched for time I'd go Pinkerton's.
Just don't want you to think you are going to roll of downtown at 3:30 PM and make it to Killen's in 30 minutes on a weekday. You hit gridlock fast and will be in traffic for an hour.