serious

On me travels.

This weekend coming I'll be in London. Next week I'll be in Leeds until the weekend, at which point I'll be back in Edinburgh.

What is there worth doing in Leeds?
Well, shop if you like that sorta thing. Their Corn Exchange is a temple of the unneeded, gaudiness and tat.
The Corn Exchange is good. Also, there's a sort of alternative what's on flyer sheet for Leeds which is handed out at places like the Corn Exchange, and that will have details of record shops and other interesting things.

Also, Granary Wharf (google for it, I guess - it's very close to the station) at least used to be alright for shopping, if a bit full of headshops and painted wooden hippy tat. Spectacular Victorian vaulting though: it really needs to be used as a film noir set.

Victoria Quarter is good for shopping, too, although of a more mainstream sort, and there's Harvey Nicks in the centre, although I'm not sure if that's your sort of thing exactly.

There used to be an Interesting Record Shop called IIRC Vinyl Tap on a side street reasonably close to the Corn Exchange, although whether it's still there I couldn't say. Actually, there's a cheap'n'dodgy record shop in the basement of the Corn Exchange itself (or there was last time I was there), but I doubt if it would have very much that you'd be interested in.

As to traditional tourist attractions, there's the Royal Armouries, if you've got a bit of time. I've never visited, but they're supposed to be excellent.
I'm pretty sure that Vynil Tap has gone, unfortunately.

When did you last visit Granary Wharf? If it was longer than five years ago, I expect you'd be horribly disappointed with it now.

I'd second the recommendation for the Royal Armouries though.
Gah! Why do I have this persistent inability to spell the word Vinyl?! It's right there in front of me and I still get it wrong! Vinyl! Vinyl! Vinyl! Gah!
I can't remember the occasion of my last visit to GW, but it was almost certainly a fair while back. I seem to recall it was going swiftly downhill even back then. Is it dreadful now? I hope, at any rate, that all the quite voluptuously cinematographic water-filled vaults are still there.
The water-filled vaults remain thankfully intact, but the market at the back has been turned into a soul-less corporate tat-factory.