Can't let an error like that go unanswered, Mike! Actually, Vilnius has a much more Polish influence. There are some Russians, but Lithuanian-born Poles and native Lithuanians far outnumber them. Kaunas is considered (within the country itself) the most "purely" Lithuanian city, as it was the capital for a while, when Vilnius was under Polish control. Strange history, but fascinating if you can sort it all out.
It takes about 2 hours by regular bus between Vilnius and Kaunas, or you can get a microbus which usually takes about 1 1/2 hours but costs a little more. Pick up microbuses at the main bus terminal, they usually are yellow and pick up to one side of the terminal - just ask for "mikrobusas i Vilniu" and you should get pointed in the right direction. If you leave early, you can easily make a daytrip to Vilnius.
We only visited Kaunas once, but found it quite an interesting place - the MK Ciurlonis museum in back of the Military Museum is well worth the visit, even if the pictures are copies. Some people really like the Devil (or Witches) Museum, I was not overwhelmed. Take a walk down to the river, there are some great old churches and one hosts an art gallery. Another place that intrigued us was the music museum, but despite our arrival during the "open" hours, we couldn't figure out how to get in...round the back there are some cool sculptures and stuff. Like Vilnius, it's fun to just kind of wander down back streets and see what treasures you stumble on. Kaunas struck me as more of an industrial/business centre - a lot of businesses have their offices here, and it doesn't have the same kind of sprawling Old Town as Vilnius, though the pedestrian area of the Old Town is quite pleasant.
Near Kaunas is Rumsiskis, which is an open air museum of architecture, but they also have craftspeople, traditional food at the cafe, and even a couple of cattle cars in which Lithuanians were deported to Siberia. Double check at tourist info, but I think you can get a regular bus from the station.
The only place I recall at which we ate was on the main drag, a big, glass enclosed restaurant with a huge salad bar, close to the Theatre. The staff spoke English and the food was pretty good - not the best ever, but good enough. I believe they served a decent breakfast, but I could be confusing it with somewhere else. We were there this same time of year, it was pretty wet and cold already, though we didn't have snow yet.
I guess being a Ryanair hub, you won't completely avoid the stags, but hopefully late October isn't the prime time for those types of parties!
Have fun, I'm jealous.