Kazbegi is a very small town that shuts down when the sun goes down. There are no real pubs or spots to meet other travellers other than meeting up with them at the homestays around town. You can hang around the square in the evening if you want to meet locals but chances are you will only meet drunk Russians dressed in black and they can get rowdy from time to time. Grab a good book to take with you or take a few beers because this town really shuts down.
Nightlife in Kazbegi consists of smoking on the hotel steps with unshaven men in dark suits, drinking copious amounts of vodka with those same men, or watching Georgian television while tucking into a hearty meal of halva and peanuts, swigging on a bottle of something green and fizzy. Georgian television is quite an acquired taste, probably one you're not going to fully acquire if you don't speak Georgian. The news seems to last for two hours, broken up every ten minutes for a "reklama" advert break. Then there are the soaps, shipped in from Brazil and dubbed into Georgian. These are quite watchable, especially with some Kazbegi beer to help it down, and entertaining for a while until you realise that there are only two dubbing artists, one male and one female, for the entire cast. The all female arguments lost some of their clout, all parts read out by the same bored-sounding woman. A Russian music channel faded in and out for a bit, before vanishing in fog and crackle. Bring a good book or a notepad and pen, or buy enough local beer or vodka and make your own entertainment.
Dress Code: For smoking on the steps, you can try to fit in by not shaving for a week or so and wearing black. Anything black will do, so long as it keeps you warm enough without making you look pathetic and unused to mountain climes. An ability to chain smoke and hold your drink would help also.
For watching the telly, you'll need a sense of humour and enough vodka or beer to make the programmes entertaining. As for dress code, well, the central heating should be blasting on full in the evening, so you'll feel overdressed even in the skimpiest of clothing.