All three are nice.
Flamingo is desirable because it's center of the strip. The units are good sized and as stated, many have been renovated of late. Flamingo also has access to the Flamingo hotel pools, but as has been stated, baring a sudden freak heat wave those pools won't be of any use to you in January. The monorail station is less than a stones throw away from the HGVC property.
"The Strip" is at the north end not far from Rivera, Sahara and Circus Circus for reference. It's the newest and most posh property of the three with nice excercise and spa facilities. It's furthest removed from the center of the strip, but just across the street from a new complex (Fontain Blu) scheduled to open sometime in 2009.
HGVC LV Hilton (aka Karen) isn't as spit and polished as the strip property, is smaller and off the strip. Still, it's very nice and I stay here often as it's close to the convention center and the monorail. It's only slightly removed from the glitz of the strip which is easily accessible via monorail or car and has the LV Hilton next door, just a couple minute walk from whatever you crave from the facility there. It's a nice balance. Of the three, self parking is the easiest here and cabs are usually readily available or a minute or two's wait after a call from the desk.
Simply for it's central location and proximity to your meeting, the Flamingo would be a no brainer but it would be hard to go wrong with any of them really.