This answer is from my experience having just lived seven and a half months in Georgia, mostly in Tbilisi but also for a month and a half in Batumi.
Yes Russian is widely known and used every day by the majority of people in Georgia aged in their 20's and above.
Most people are fluent (they can talk quickly without translating in their heads) but would make lots of grammatical errors that native Russian speakers would pick up.
In fact many people love the Russian language and tell me how beautiful it is. (I'm Australian so they're not just being nice to me.)
Certain words are exceptionally common even when otherwise speaking Georgian. Some that come to mind are "маршрутка", "молодец", "похмелье" meaning "hangover", even though there are often native words like ნაბახუსევი (nabakhusevi) for "hangover" and ყოჩაღ (qochagh) for "bravo", etc. I've also come across "изжога", "в общем", and "именно" mixed in with Georgian.
There are some shops I go to regularly where the staff speak Georgian and know that I know more Georgian than Russian, yet they always talk to me in Russian and I always respond in Georgian! (-:
But children are no longer being taught Russian in school and there is a two-year-old program which imports hundreds of native English speakers to work as English teachers in towns and villages throughout the country.
My impression is that people still perceive Russian to be "cool" along with English. All of my friends listen to both English and Russian music, but none of them listen to Georgian music. So I assume younger people will continue to pick up Russian without being taught for some time yet, but I would expect the quality to continue to decline.