The Cockpit is head and shoulders the best
Wednesday night they have "Panic" and Friday they have "Session", these are the best nights, they tend to have one room with more classic stuff like Stone Roses, Oasis, Pulp, Blur, Inspiral Carpets, New Order, Joy Division, Happy Mondays etc and another room playing Libertines, Kaiser Chiefs, The Coral, Kasabian, The Music, Franz Ferdinand and so on
Star - one room of metal and punk, another room of indie. Music not bad, although not as good as the Cockpit but the thing with Star is it tends to be very much a 1st year student type thing so has a school-disco feel to it with teenagers wandering round trying to pull each other. Cockpit is a bit more underground and hard core ish and has a lot more locals and tends to be a bit older in profile. I guess if you're only casual indie fan Star would be a more fun night out because Cockpit can seem a bit full on.
The Bassment, Bar Phono in the Merrion Centre do some indie nights, Fuzzy Logic on Thursdays at Bassment for example. On weekends Bar Phono tends to be a bit goth-mosher.
Think Tank? is smallish club that does some decent nights
but yeah, Leeds does have a good indie scene
just bear in mind if someone tells you "Creation has an indie room on a Wednesday", its the crappest place in Leeds