Oh there are loads of bars in leeds! We went there for my friends hen weekend and we didnt know the town at all but we still found plenty of good places.
http://www.leeds-uk.com/bars.htm
Maybe start at Wetherspoons or Yates or something as they're good places to start off with cheap drinks. We started in Wetherspoons and got some food in there too. Or how about booking an indian restaurant or something for the friday night? Like for about 9.30pm so you can go for few drinks before and then out again afterwards but it'll sort of break the night up.
If you fancy camping it up then try
http://www.birdcagelive.com/
Its a drag/caberet club and we went and loved every minute of it! But its very camp and OTT so maybe not so good if any of your brothers friends wouldnt like that sort of stuff.
Have you spoken to your brother about what he would like and what he wouldnt like? I dont think it really matters about his friends as its not their stag party. When S has his stag party the guys bought him a giant condom that he had to wear on his head and handcuffs and random stuff like that but he was drunk so loved it. Haha.
As for transport you could just look up train prices and then let everyone buy their own ticket. Try
www.thetrainline.com/
The dogs will be a good night out. We went there a while ago on a work night out and it was very fun. There was a few different rules when it came to betting though but we got an information sheet with our tickets.
Oh i found the terms
http://www.dog-track.co.uk/stakes_odds.shtml I usually put each way bets on because you had more chance of winning something! Although i spent £12 and won £8 so not really good idea to take advice off me!