Quiet, free meeting place in the centre of Leeds?

I need to establish a quiet meeting place in the centre of Leeds where four of us can meet on early evenings roughly once a month to discuss a project we're working on. It needs to be quiet enough that we can hold a conversation while private enough that we can't be overheard. Once we start making money we'll use the facilities at One Aire Street but at £25 per hour plus VAT for their meeting rooms their pricing is a little too strong for us while we're not making anything.

Does anyone have any suggestions as to where we could meet? We don't mind paying for drinks, food, etc. to justify our presence if it's a pub or similar. All that matters is that it's quiet and reasonably private. We've been using the lobby at a big hotel off the M1, which has served the purpose perfectly, but we recently added a new member to the team for whom that location really doesn't work.

Do hotels mind you doing this kind of thing if you're not actually staying there? The one we've used before (off the M1) seemed fine with us being there but there was nothing anywhere in their literature saying whether you could drop in for a drink and a bite to eat if you weren't actually staying there - we just turned up and hoped no one objected!

Always happy to play fair by spending money on drinks and food so I guess we should be fine.

Clayton hotel, used to be called Bewley's hotel. Easy to get to by car, on street parking round the corner, far enough outside the city centre to be nice and quiet, buy a pot of tea or a coffee and they will leave you in peace. I used to work in a building next to the hotel and we'd have all our meetings in the foyer. IIRC they also had free wifi, but that was a good few years ago now.