I'm a student in Leeds and have been to loads.. I'll give you a little run through here of my top choices with (from what I can remember) a rough price.
Simply Exquisite, one of the best meals I've ever eaten. I hada Valentines set menu with my girlfriend which was rather pricey but amazing. The actual place is incredible as well, really nice. Friendly service and if you're willing to splurge on a special occasion my number 1.
Won 'best independent Italian restaurant' on Gordon Ramsay's F Word. Again great food at a slightly cheaper price than San Carlo. Only downside is you can't book. You just turn up on the night and then they have an upstairs bar area that you can get a drink and some nibbles at while you wait 30-45 mins for a table.
One of Jamie Oliver's Italian restaurants, I have never eaten here myself so I can't give you a first hand review. I have however been told it is a good solid eat and at a reasonable price. But as I said, I couldn't confirm that (maybe a quick browse of the site would help you)
Brilliant steakhouse, there are a few dotted around the country and if anyone has been to 'grill on the alley' in Manchester they will be able to tell you how good the steaks here are. Best steak I've had in Leeds, so if it's steak you're after I'd recommend you look no further. Steer clear of the burgers.. the steaks are much better cuts of meat. You pay what you'd expect to pay at a dedicated steakhouse, it's certainly not pub prices.
Standard chain Browns, decent food at decent prices. Been here a few times, never been disappointed but at the same time it has never set my world alight. Good service though.
Red Hot World Buffet
Bit of a wildcard lol. A huge buffet restaurant that has every cuisine you could want. The food doesn't taste like buffet food either it tastes as though you'd ordered it fresh at a restaurant. It's incredible and all for £13-£15. It's not particularly posh so maybe not right for your occasion but if you're ever back in Leeds I recommend it, it has to be seen/tasted/experienced to be believed.
If you want any more info then feel free to PM me or reply on here. I know plenty more if none of these suit your needs but I'd say San Carlo or Salvo's will definitely not disappoint you. Also don't let it worry you that I'm a student I'm rather well travelled and I assure you these are not a bunch of cheap student dives