I used to commute by car from that general area to midtown - (east side in the 30s). LIE to midtown tunnel. From the tunnel, I was maybe 6 blocks from the parking lot.
Some years ago it took me 60-90 minutes each way. Add more for snow, rain, holiday weekend, UN event, President in town, etc.. It's horrible at first, but you do get used to it.
These days, my impression is that traffic is worse. I would guess a little longer. Some of the time depends on where in Manhattan you are going. If you park near the tunnel (or a bridge) you will save time. If you have to navigate the streets it will be worse. If you need to get to/from the West side, forget about it. Crosstown traffic is a nightmare.
"Gibson Station" mentioned 40 minutes in non-rush hours. I would agree with that. The problem is that "rush hour" is most of the day. 6am-10am is normal rush hour. 10am-3pm is when all the commercial traffic gets on the road because they avoid the normal rush. 3pm is when the schools let out, and that leads into the evening rush which lasts until about 7pm.
If there is a game at Shea (Citi Field to the rest of you) that extends the rush through that bottleneck.
Weekends bring their own traffic snarls as people get in and out of the city.
Not trying to paint a doom and gloom picture. Coming from Atlanta you should be no stranger to traffic. It is what it is.
Best routes depend on where in the city you are going (parking).
From Brookville the LIE (495) is your best bet. Even better through Nassau if you can use the HOV lane. The Northern State Parkway (NSP) provides an alternative. Traffic is sometimes better on one than the other.
Once you hit Flushing, you have some options. For the Midtown Tunnel and points south, you stay on the LIE. For the Triboro (now the RFK bridge) you get onto the Grand Central (which the NSP turns into).
Closer to the city on the LIE, you can get on the BQE to get to the bridges for lower Manhattan. Right before the Midtown Tunnel, you can exit the LIE to access the Queensboro Bridge (59th street).
There are numerous "alternate" routes and ways to get around. These are just the most direct routes.
Years of driving these roads can be murder on a car. On the plus side, you can catch up on audiobooks while you drive.
If you plan to drive, allow me to offer a suggestion:
Drive to Flushing. There are places to park around Citi Field. That leaves you at the "7" subway line which is a direct shot into Grand Central station (42nd street/Park Ave) or Times Square. From there you can transfer to a subway for anywhere else in the city.
If you want to be more adventurous, you can drive further on the LIE into Long Island City. There are parking lots near the "Vernon-Jackson" stop for the "7" line. From there it is one stop to Grand Central, two to Times Square. Five minutes to Manhattan on the train vs. 20-30 min (or more) by car.
This gives you the convenience of a car, while avoiding all the extra hassle (and cost) of driving and parking in Manhattan.