One thing- reserve a reputable car service (as I’ve been employed as an assistant in a few wall st. and park ave firms, I’ve always used limores and they’ve always been very reliable) a few days in advance. Good car service to airports can fill up quickly, ESPECIALLY this time of year- that is, unless your firm has a cache of cars reserved only for them.
I don’t know if they still do it, but I’ve taken a water taxi from La Guardia to Midtown. This was 15 years ago. It got me there fast, and no traffic lights!
Here’s a USAToday article from, apparently, 2005:
http://www.usatoday.com/travel/flights/today/2005-01-21-sky-archivejan20_x.htm
Why is everyone acting like Queens is on the moon or something? Some of us do actually take the 7 train and get to work one time.
And getting a yellow cab along the major boulevards is pretty easy. And since when aren’t cabs supposed to pick up fares in Queens? I’ve never heard of this. I take them all the time, are you saying they are committing some offense?
That being said, for business travel I would just take a car service 
Call one up ahead of time to pick you up. In the middle of the day, traffic won’t be too too bad.
I was just looking at the TLC rules, and there is nothing prohibiting yellow cabs from taking hails in Queens. There are rules about where taxis may be hailed, but no blanket borough-wide restrictions on hailing cabs or taxis soliciting passengers.
That said, finding cabs to hail in the outer boroughs is not necessarily an easy task. There are a few taxi stands, and it is very much hit-or-miss outside of that. Take a limo or cab to the airport - likely quicker than the subway.
Was wondering about this as well, I presume what friedo meant is that gypsy cabs** are not supposed to take hails and the the majority of cabs in the boroughs are actually gypsy cabs. IME gypsy cab drivers pretty much ignored the rule — 61st Street in Woodside, by the 7 train and LIRR, was effectively a gypsy cab stand when I lived there '01-'03.
I also used to live in Astoria, I would see yellow cabs go down Astoria Blvd fairly often. But for OP’s route I agree that the 2 best routes via public transit are those listed by friedo, with the shuttle from Grand Central being the faster option. I loved that bus, what’s nice is that if you have a 10 minute wait until the next bus, you can go inside Grand Central, buy a coffee, and stare at the ceiling. That being said, 2:30 for a 4:30 flight is cutting it close – I would probably take the shuttle because I live on the edge like that, but I wouldn’t recommend it to a business traveler.
**a cab that is not yellow and does not have a medallion, a hired Town Car
Last time I checked, you can’t get to LaGuardia on the 7. 
Hey, I didn’t say it actually goes a lot of places. Just that it does get to where it’s supposed to 
Anyway I instinctively have to defend the 7 when people rag on it. I get flashbacks of John Rocker.
Don’t sweat it, bro. I used to live in Flushing. Back before the #7 got the R62s, too. Old-skool representin’.
Astoria is much nicer. 
I lived there four times as long.
Plan B, your company doesn’t arrange airport transportation as part of your travel?
If they don’t just ask whatever company you are visiting to recomend a car service and they’ll probably have someone set it up for you.