Kawaramachi is the city centre, you'll find all the shops, bars, etc. there. The Hub is a nice pub, Pig and Whistle also. Nearby the Hub you'll find Bar Isn't It, a club full of foreigners usually. Places to eat: Shakey's all you can eat pizza, pasta, salad. A bit nasty, but cheap. Around 900 yen. Also check out Bikkuri Donkey, I thought it was quite fun! There are many choices where to eat or drink, shouldn't be a prob. Shopping: check out a long covered mall, Angel Street I think it is called. If you need a sports shop, Mitsuhashi Sports has it all. Anyway, there are shops all over Kawaramachi!
There is this other lively area called Saiin. Much smaller than Kawaramachi though. There are some good karaoke places, cafes.
Sightseeing wise, I highly recommend Sanjusangendo. One of the most impressive temples around! Also check out Ryoanji. Nice place. Okazaki Area is also worth a visit. It has quite a few art galleries, museums, a zoo and a shrine called Heian Jingu. Basically, Kyoto has everything in terms of sightseeing. It's just the matter of what you want to see really and having enough time to do it!